A Gray code based gradient-free optimization(GCO)algorithm is proposed to update the parameters of parameterized quantum circuits(PQCs)in this work.Each parameter of PQCs is encoded as a binary string,named as a gene,...A Gray code based gradient-free optimization(GCO)algorithm is proposed to update the parameters of parameterized quantum circuits(PQCs)in this work.Each parameter of PQCs is encoded as a binary string,named as a gene,and a genetic-based method is adopted to select the offsprings.The individuals in the offspring are decoded in Gray code way to keep Hamming distance,and then are evaluated to obtain the best one with the lowest cost value in each iteration.The algorithm is performed iteratively for all parameters one by one until the cost value satisfies the stop condition or the number of iterations is reached.The GCO algorithm is demonstrated for classification tasks in Iris and MNIST datasets,and their performance are compared by those with the Bayesian optimization algorithm and binary code based optimization algorithm.The simulation results show that the GCO algorithm can reach high accuracies steadily for quantum classification tasks.Importantly,the GCO algorithm has a robust performance in the noise environment.展开更多
To compress hyperspectral images, a low complexity discrete cosine transform （DCT）-based distributed source coding （DSC） scheme with Gray code is proposed. Unlike most of the existing DSC schemes, which utilize tr...To compress hyperspectral images, a low complexity discrete cosine transform （DCT）-based distributed source coding （DSC） scheme with Gray code is proposed. Unlike most of the existing DSC schemes, which utilize transform in spatial domain, the proposed algorithm applies transform in spectral domain. Set-partitioning-based approach is applied to reorganize DCT coefficients into waveletlike tree structure and extract the sign, refinement, and significance bitplanes. The extracted refinement bits are Gray encoded. Because of the dependency along the line dimension of hyperspectral images, low density paritycheck-（LDPC）-based Slepian-Wolf coder is adopted to implement the DSC strategy. Experimental results on airborne visible/infrared imaging spectrometer （AVIRIS） dataset show that the proposed paradigm achieves up to 6 dB improvement over DSC-based coders which apply transform in spatial domain, with significantly reduced computational complexity and memory storage.展开更多
We developed a novel absolute multi-pole encoder structure to improve the resolution of the multi-pole encoder, realize absolute output and reduce the manufacturing cost of the encoder. The structure includes two ring...We developed a novel absolute multi-pole encoder structure to improve the resolution of the multi-pole encoder, realize absolute output and reduce the manufacturing cost of the encoder. The structure includes two ring alnicos defined as index track and sub-division track, respectively. The index track is magnetized based on the improved gray code, with linear halls placed around the track evenly. The outputs of linear halls show the region the rotor belongs to. The sub-division track is magnetized to N-S-N-S (north-south-north-south), and the number of N-S pole pairs is determined by the index track. Three linear hall sensors with an air-gap of 2 mm are used to translate the magnetic filed to voltage signals. The relative offset in a single N-S is obtained through look-up. The magnetic encoder is calibrated using a higher-resolution incremental optical encoder. The pulse output from the optical encoder and hall signals from the magnetic encoder are sampled at the same time and transmitted to a computer, and the relation between them is calculated, and stored in the FLASH of MCU (micro controller unit) for look-up. In the working state, the absolute angle is derived by looking-up with hall signals. The structure is simple and the manufacturing cost is very low and suitable for mass production.展开更多
Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to...Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to is defined which preserves self duality of linear codes. As a consequence self-dual, formally self-dual and self-orthogonal codes over are constructed. Some examples are also given to illustrate this.展开更多
This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the propertie...This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.展开更多
In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differen...In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.展开更多
By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and suffi...By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.展开更多
Background:Flight and freezing are two vital defensive behaviors that mice display to avoid natural enemies.When they are exposed to innate threats,visual cues are processed and transmitted by the visual system into t...Background:Flight and freezing are two vital defensive behaviors that mice display to avoid natural enemies.When they are exposed to innate threats,visual cues are processed and transmitted by the visual system into the emotional nuclei and finally transmitted to the periaqueductal gray(PAG)to induce defensive behaviors.However,how the dorsal PAG(dPAG)encodes the two defensive behaviors is unclear.Methods:Multi-array electrodes were implanted in the dPAG nuclei of C57BL/6 mice.Two kinds of visual stimuli(looming and sweeping)were used to induce defensive behaviors in mice.Neural signals under different defense behaviors were recorded,and the encoding characteristics of the two behaviors were extracted and analyzed from spike firing and frequency oscillations.Finally,synchronization of neural activity during the defense process was analyzed.Results:The neural activity between flight and freezing behaviors showed different firing patterns,and the differences in the inter-spike interval distribution were mainly reflected in the 2–10 ms period.The frequency band activities under both defensive behaviors were concentrated in the theta band;the active frequency of flight was~8to 10 Hz,whereas that of freezing behavior was~6 to 8 Hz.The network connection density under both defense behaviors was significantly higher than the period before and after defensive behavior occurred,indicating that there was a high synchronization of neural activity during the defense process.Conclusions:The dPAG nuclei of mice have different coding features between flight and freezing behaviors;during strong looming stimulation,fast neuro-i nstinctive decision making is required while encountering weak sweeping stimulation,and computable planning late behavior is predicted in the early stage.The frequency band activities under both defensive behaviors were concentrated in the theta band.There was a high synchronization of neural activity during the defense process,which may be a key factor triggering different defensive behaviors.展开更多
The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the...The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the nonlinear code constructed by Goethals in 1976.展开更多
Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub&g...Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.展开更多
In this paper, the structure of the non-chain ring Z15 is studied. The ideals of the ring Z15 are obtained through its non-units and the Lee weights of elements in Z15 are presented. On this basis, by the Chinese Rema...In this paper, the structure of the non-chain ring Z15 is studied. The ideals of the ring Z15 are obtained through its non-units and the Lee weights of elements in Z15 are presented. On this basis, by the Chinese Remainder Theorem, we construct a unique expression of an element in Z15. Further, the Gray mapping from Zn15 to Z2n15 is defined and it’s shown to be distance preserved. The relationship between the minimum Lee weight and the minimum Hamming weight of the linear code over the ring Z15 is also obtained and we prove that the Gray map of the linear code over the ring Z15 is also linear.展开更多
Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray map...Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Z_(4) are cyclic,quasi-cyclic or permutation equivalent to this code.For an odd positive integer n,we determine the generator polynomials of cyclic and Λ-constacyclic codes of length n over R.Further,we prove that a(θ,Λ)-cyclic code of length n is a Λ-constacyclic code if n is odd,and a Λ-quasi-twisted code if n is even.A few examples are also incorporated,in which two parameters are new and one is best known to date.展开更多
Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of app...Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of applying the basic theory of symbolic dynamics to the measurement is presented and proved. Then, the theoretical model of chaotic transducer is realized by using the switched capacitor and the basic experimental results are given. The transducer has such characters as high sensitivity, resolution, the simple structure and combining signal amplification with A/D. The new area of the application of chaos is exploited. Meanwhile, it provides a new method of exploring the structure of new type transducer.展开更多
Based on the coded and non-coded targets, the targets are extracted from the images according to their size, shape and intensity etc., and thus an improved method to identify the unique identity（D） of every coded ta...Based on the coded and non-coded targets, the targets are extracted from the images according to their size, shape and intensity etc., and thus an improved method to identify the unique identity（D） of every coded target is put forward and the non-coded and coded targets are classified. Moreover, the gray scale centroid algorithm is applied to obtain the subpixel location of both uncoded and coded targets. The initial matching of the uncoded target correspondences between an image pair is established according to similarity and compatibility, which are based on the ID correspondences of the coded targets. The outliers in the initial matching of the uncoded target are eliminated according to three rules to finally obtain the uncoded target correspondences. Practical examples show that the algorithm is rapid, robust and is of high precision and matching ratio.展开更多
In this paper, we study λ-constacyclic codes over the ring R = Z4 ＋ uZ4, where u^2 = 0, for λ= 1 ＋ 3u and 3 ＋ u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic cod...In this paper, we study λ-constacyclic codes over the ring R = Z4 ＋ uZ4, where u^2 = 0, for λ= 1 ＋ 3u and 3 ＋ u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over Z4. Moreover, we present many examples of λ-constacyclic codes over R whose Z4-images have better parameters than the currently best-known linear codes over Z4.展开更多
A 3D surface reconstruction method using a binocular stereo vision technology and a coded structured light,which combines a gray code with phase-shift has been studied.The accuracy of the 3 D surface reconstruction ma...A 3D surface reconstruction method using a binocular stereo vision technology and a coded structured light,which combines a gray code with phase-shift has been studied.The accuracy of the 3 D surface reconstruction mainly depends on the decoding of gray code views and phase-shift views.In order to find the boundary accurately,gray code patterns and their inverses are projected onto a human eye plaster model.The period dislocation between the gray code views and the phase-shift views in the course of decoding has been analyzed and a new method has been proposed to solve it.The splicing method is based on feature points.The result of the 3D surface reconstruction shows the accuracy and reliability of our method.展开更多
We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cycli...We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2.展开更多
This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^...This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.61871234 and 62375140)Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX190900).
文摘A Gray code based gradient-free optimization(GCO)algorithm is proposed to update the parameters of parameterized quantum circuits(PQCs)in this work.Each parameter of PQCs is encoded as a binary string,named as a gene,and a genetic-based method is adopted to select the offsprings.The individuals in the offspring are decoded in Gray code way to keep Hamming distance,and then are evaluated to obtain the best one with the lowest cost value in each iteration.The algorithm is performed iteratively for all parameters one by one until the cost value satisfies the stop condition or the number of iterations is reached.The GCO algorithm is demonstrated for classification tasks in Iris and MNIST datasets,and their performance are compared by those with the Bayesian optimization algorithm and binary code based optimization algorithm.The simulation results show that the GCO algorithm can reach high accuracies steadily for quantum classification tasks.Importantly,the GCO algorithm has a robust performance in the noise environment.
基金supported by the National Natural Science Foundationof China (60702012)the Scientific Research Foundation for the Re-turned Overseas Chinese Scholars, State Education Ministry
文摘To compress hyperspectral images, a low complexity discrete cosine transform （DCT）-based distributed source coding （DSC） scheme with Gray code is proposed. Unlike most of the existing DSC schemes, which utilize transform in spatial domain, the proposed algorithm applies transform in spectral domain. Set-partitioning-based approach is applied to reorganize DCT coefficients into waveletlike tree structure and extract the sign, refinement, and significance bitplanes. The extracted refinement bits are Gray encoded. Because of the dependency along the line dimension of hyperspectral images, low density paritycheck-（LDPC）-based Slepian-Wolf coder is adopted to implement the DSC strategy. Experimental results on airborne visible/infrared imaging spectrometer （AVIRIS） dataset show that the proposed paradigm achieves up to 6 dB improvement over DSC-based coders which apply transform in spatial domain, with significantly reduced computational complexity and memory storage.
基金Funded partly by Heilongjiang Province Financial Fund for Researchers Returning from Abroad
文摘We developed a novel absolute multi-pole encoder structure to improve the resolution of the multi-pole encoder, realize absolute output and reduce the manufacturing cost of the encoder. The structure includes two ring alnicos defined as index track and sub-division track, respectively. The index track is magnetized based on the improved gray code, with linear halls placed around the track evenly. The outputs of linear halls show the region the rotor belongs to. The sub-division track is magnetized to N-S-N-S (north-south-north-south), and the number of N-S pole pairs is determined by the index track. Three linear hall sensors with an air-gap of 2 mm are used to translate the magnetic filed to voltage signals. The relative offset in a single N-S is obtained through look-up. The magnetic encoder is calibrated using a higher-resolution incremental optical encoder. The pulse output from the optical encoder and hall signals from the magnetic encoder are sampled at the same time and transmitted to a computer, and the relation between them is calculated, and stored in the FLASH of MCU (micro controller unit) for look-up. In the working state, the absolute angle is derived by looking-up with hall signals. The structure is simple and the manufacturing cost is very low and suitable for mass production.
文摘Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to is defined which preserves self duality of linear codes. As a consequence self-dual, formally self-dual and self-orthogonal codes over are constructed. Some examples are also given to illustrate this.
文摘This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.
文摘In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.
基金Supported by the National Natural Science Foundation of China(No.61370089)
文摘By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.
基金National Natural Science Foundation of China,Grant/Award Number:U2004152Science and Technology Department of Henan Province,Grant/Award Number:192102310026 and 224200510001。
文摘Background:Flight and freezing are two vital defensive behaviors that mice display to avoid natural enemies.When they are exposed to innate threats,visual cues are processed and transmitted by the visual system into the emotional nuclei and finally transmitted to the periaqueductal gray(PAG)to induce defensive behaviors.However,how the dorsal PAG(dPAG)encodes the two defensive behaviors is unclear.Methods:Multi-array electrodes were implanted in the dPAG nuclei of C57BL/6 mice.Two kinds of visual stimuli(looming and sweeping)were used to induce defensive behaviors in mice.Neural signals under different defense behaviors were recorded,and the encoding characteristics of the two behaviors were extracted and analyzed from spike firing and frequency oscillations.Finally,synchronization of neural activity during the defense process was analyzed.Results:The neural activity between flight and freezing behaviors showed different firing patterns,and the differences in the inter-spike interval distribution were mainly reflected in the 2–10 ms period.The frequency band activities under both defensive behaviors were concentrated in the theta band;the active frequency of flight was~8to 10 Hz,whereas that of freezing behavior was~6 to 8 Hz.The network connection density under both defense behaviors was significantly higher than the period before and after defensive behavior occurred,indicating that there was a high synchronization of neural activity during the defense process.Conclusions:The dPAG nuclei of mice have different coding features between flight and freezing behaviors;during strong looming stimulation,fast neuro-i nstinctive decision making is required while encountering weak sweeping stimulation,and computable planning late behavior is predicted in the early stage.The frequency band activities under both defensive behaviors were concentrated in the theta band.There was a high synchronization of neural activity during the defense process,which may be a key factor triggering different defensive behaviors.
文摘The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the nonlinear code constructed by Goethals in 1976.
文摘Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.
文摘In this paper, the structure of the non-chain ring Z15 is studied. The ideals of the ring Z15 are obtained through its non-units and the Lee weights of elements in Z15 are presented. On this basis, by the Chinese Remainder Theorem, we construct a unique expression of an element in Z15. Further, the Gray mapping from Zn15 to Z2n15 is defined and it’s shown to be distance preserved. The relationship between the minimum Lee weight and the minimum Hamming weight of the linear code over the ring Z15 is also obtained and we prove that the Gray map of the linear code over the ring Z15 is also linear.
文摘Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Z_(4) are cyclic,quasi-cyclic or permutation equivalent to this code.For an odd positive integer n,we determine the generator polynomials of cyclic and Λ-constacyclic codes of length n over R.Further,we prove that a(θ,Λ)-cyclic code of length n is a Λ-constacyclic code if n is odd,and a Λ-quasi-twisted code if n is even.A few examples are also incorporated,in which two parameters are new and one is best known to date.
文摘Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of applying the basic theory of symbolic dynamics to the measurement is presented and proved. Then, the theoretical model of chaotic transducer is realized by using the switched capacitor and the basic experimental results are given. The transducer has such characters as high sensitivity, resolution, the simple structure and combining signal amplification with A/D. The new area of the application of chaos is exploited. Meanwhile, it provides a new method of exploring the structure of new type transducer.
基金The National Natural Science Foundation of China(No50475041)
文摘Based on the coded and non-coded targets, the targets are extracted from the images according to their size, shape and intensity etc., and thus an improved method to identify the unique identity（D） of every coded target is put forward and the non-coded and coded targets are classified. Moreover, the gray scale centroid algorithm is applied to obtain the subpixel location of both uncoded and coded targets. The initial matching of the uncoded target correspondences between an image pair is established according to similarity and compatibility, which are based on the ID correspondences of the coded targets. The outliers in the initial matching of the uncoded target are eliminated according to three rules to finally obtain the uncoded target correspondences. Practical examples show that the algorithm is rapid, robust and is of high precision and matching ratio.
文摘In this paper, we study λ-constacyclic codes over the ring R = Z4 ＋ uZ4, where u^2 = 0, for λ= 1 ＋ 3u and 3 ＋ u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over Z4. Moreover, we present many examples of λ-constacyclic codes over R whose Z4-images have better parameters than the currently best-known linear codes over Z4.
文摘A 3D surface reconstruction method using a binocular stereo vision technology and a coded structured light,which combines a gray code with phase-shift has been studied.The accuracy of the 3 D surface reconstruction mainly depends on the decoding of gray code views and phase-shift views.In order to find the boundary accurately,gray code patterns and their inverses are projected onto a human eye plaster model.The period dislocation between the gray code views and the phase-shift views in the course of decoding has been analyzed and a new method has been proposed to solve it.The splicing method is based on feature points.The result of the 3D surface reconstruction shows the accuracy and reliability of our method.
基金Foundation item： Supported by the Scientific Research Foundation of Education Department of Hubei Province（B2013069） Supported by the National Science Foundation of Hubei Polytechnic University of China （12xjzl4A, llyjz37B）
文摘We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2.
基金supported by the National Natural Science Foundation of China under Grant Nos.61672036 and 61202068the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2015D11+1 种基金Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133Key projects of support program for outstanding young talents in Colleges and Universities under Grant No.gxyq ZD2016008
文摘This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.
