The Experts below are selected from a list of 5454 Experts worldwide ranked by ideXlab platform
Tao Xiang - One of the best experts on this subject based on the ideXlab platform.
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period distribution of the generalized discrete arnold cat map for n 2 e
IEEE Transactions on Information Theory, 2013Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:The Arnold cat map is employed in various applications where chaos is utilized, especially chaos-based cryptography and watermarking. In this paper, we study the problem of period distribution of the generalized discrete Arnold cat map over the Galois Ring \BBZ2e. Full knowledge of the period distribution is obtained analytically by adopting the Hensel lift approach. Our results have impact on both chaos theory and its applications as they not only provide design strategy in applications where special periods are required, but also help to identify unstable periodic orbits of the original chaotic cat map. The method in our paper also shows some ideas how to handle problems over the Galois Ring \BBZ2e.
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period distribution of generalized discrete arnold cat map for n p e
IEEE Transactions on Information Theory, 2012Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:In this paper, we analyze the period distribution of the generalized discrete cat map over the Galois Ring where is a prime. The sequences generated by this map are modeled as 2-dimensional LFSR sequences. Employing the generation function and the Hensel lifting approaches, full knowledge of the detail period distribution is obtained analytically. Our results not only characterize the period distribution of the cat map, which gives insights to various applications, but also demonstrate some approaches to deal with the period of a polynomial in the Galois Ring.
Fei Chen - One of the best experts on this subject based on the ideXlab platform.
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period distribution of the generalized discrete arnold cat map for n 2 e
IEEE Transactions on Information Theory, 2013Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:The Arnold cat map is employed in various applications where chaos is utilized, especially chaos-based cryptography and watermarking. In this paper, we study the problem of period distribution of the generalized discrete Arnold cat map over the Galois Ring \BBZ2e. Full knowledge of the period distribution is obtained analytically by adopting the Hensel lift approach. Our results have impact on both chaos theory and its applications as they not only provide design strategy in applications where special periods are required, but also help to identify unstable periodic orbits of the original chaotic cat map. The method in our paper also shows some ideas how to handle problems over the Galois Ring \BBZ2e.
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period distribution of generalized discrete arnold cat map for n p e
IEEE Transactions on Information Theory, 2012Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:In this paper, we analyze the period distribution of the generalized discrete cat map over the Galois Ring where is a prime. The sequences generated by this map are modeled as 2-dimensional LFSR sequences. Employing the generation function and the Hensel lifting approaches, full knowledge of the detail period distribution is obtained analytically. Our results not only characterize the period distribution of the cat map, which gives insights to various applications, but also demonstrate some approaches to deal with the period of a polynomial in the Galois Ring.
Kwokwo Wong - One of the best experts on this subject based on the ideXlab platform.
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period distribution of the generalized discrete arnold cat map for n 2 e
IEEE Transactions on Information Theory, 2013Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:The Arnold cat map is employed in various applications where chaos is utilized, especially chaos-based cryptography and watermarking. In this paper, we study the problem of period distribution of the generalized discrete Arnold cat map over the Galois Ring \BBZ2e. Full knowledge of the period distribution is obtained analytically by adopting the Hensel lift approach. Our results have impact on both chaos theory and its applications as they not only provide design strategy in applications where special periods are required, but also help to identify unstable periodic orbits of the original chaotic cat map. The method in our paper also shows some ideas how to handle problems over the Galois Ring \BBZ2e.
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period distribution of generalized discrete arnold cat map for n p e
IEEE Transactions on Information Theory, 2012Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:In this paper, we analyze the period distribution of the generalized discrete cat map over the Galois Ring where is a prime. The sequences generated by this map are modeled as 2-dimensional LFSR sequences. Employing the generation function and the Hensel lifting approaches, full knowledge of the detail period distribution is obtained analytically. Our results not only characterize the period distribution of the cat map, which gives insights to various applications, but also demonstrate some approaches to deal with the period of a polynomial in the Galois Ring.
Xiaofeng Liao - One of the best experts on this subject based on the ideXlab platform.
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period distribution of the generalized discrete arnold cat map for n 2 e
IEEE Transactions on Information Theory, 2013Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:The Arnold cat map is employed in various applications where chaos is utilized, especially chaos-based cryptography and watermarking. In this paper, we study the problem of period distribution of the generalized discrete Arnold cat map over the Galois Ring \BBZ2e. Full knowledge of the period distribution is obtained analytically by adopting the Hensel lift approach. Our results have impact on both chaos theory and its applications as they not only provide design strategy in applications where special periods are required, but also help to identify unstable periodic orbits of the original chaotic cat map. The method in our paper also shows some ideas how to handle problems over the Galois Ring \BBZ2e.
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period distribution of generalized discrete arnold cat map for n p e
IEEE Transactions on Information Theory, 2012Co-Authors: Fei Chen, Kwokwo Wong, Xiaofeng Liao, Tao XiangAbstract:In this paper, we analyze the period distribution of the generalized discrete cat map over the Galois Ring where is a prime. The sequences generated by this map are modeled as 2-dimensional LFSR sequences. Employing the generation function and the Hensel lifting approaches, full knowledge of the detail period distribution is obtained analytically. Our results not only characterize the period distribution of the cat map, which gives insights to various applications, but also demonstrate some approaches to deal with the period of a polynomial in the Galois Ring.
Ling San - One of the best experts on this subject based on the ideXlab platform.
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An explicit expression for Euclidean self-dual cyclic codes of length $2^k$ over Galois Ring ${\rm GR}(4,m)$
2020Co-Authors: Cao Yuan, Cao Yonglin, Ling San, Wang GuidongAbstract:For any positive integers $m$ and $k$, existing literature only determines the number of all Euclidean self-dual cyclic codes of length $2^k$ over the Galois Ring ${\rm GR}(4,m)$, such as in [Des. Codes Cryptogr. (2012) 63:105--112]. Using properties for Kronecker products of matrices of a specific type and column vectors of these matrices, we give a simple and efficient method to construct all these self-dual cyclic codes precisely. On this basis, we provide an explicit expression to accurately represent all distinct Euclidean self-dual cyclic codes of length $2^k$ over ${\rm GR}(4,m)$, using combination numbers. As an application, we list all distinct Euclidean self-dual cyclic codes over ${\rm GR}(4,m)$ of length $2^k$ explicitly, for $k=4,5,6$
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Self-dual and complementary dual abelian codes over Galois Rings
'Journal of Algebra Combinatorics Discrete Structures and Applications', 2019Co-Authors: Jitman Somphong, Ling SanAbstract:Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes over Galois Rings are studied in terms of the ideals in the group Ring GR(pr,s)[G], where G is a finite abelian group and GR(pr,s) is a Galois Ring. Characterizations of self-dual abelian codes have been given together with necessary and sufficient conditions for the existence of a self-dual abelian code in GR(pr,s)[G]. A general formula for the number of such self-dual codes is established. In the case where gcd(∣G∣,p) = 1, the number of self-dual abelian codes in GR(p2,s), an explicit formula for the number of self-dual abelian codes in GR(p2,s)[G] are given, where the Sylow p-subgroup of G is cyclic. Subsequently, the characterization and enumeration of complementary dual abelian codes in GR(pr,s)[G] are established. The analogous results for self-dual and complementary dual cyclic codes over Galois Rings are therefore obtained as corollaries.Published versio
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Self-Dual and Complementary Dual Abelian Codes over Galois Rings
2019Co-Authors: Jitman Somphong, Ling SanAbstract:Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes over Galois Rings are studied in terms of the ideals in the group Ring ${\rm GR}(p^r,s)[G]$, where $G$ is a finite abelian group and ${\rm GR}(p^r,s)$ is a Galois Ring. Characterizations of self-dual abelian codes have been given together with necessary and sufficient conditions for the existence of a self-dual abelian code in ${\rm GR}(p^r,s)[G]$. A general formula for the number of such self-dual codes is established. In the case where $\gcd(|G|,p)=1$, the number of self-dual abelian codes in ${\rm GR}(p^r,s)[G]$ is completely and explicitly determined. Applying known results on cyclic codes of length $p^a$ over ${\rm GR}(p^2,s)$, an explicit formula for the number of self-dual abelian codes in ${\rm GR}(p^2,s)[G]$ are given, where the Sylow $p$-subgroup of $G$ is cyclic. Subsequently, the characterization and enumeration of complementary dual abelian codes in ${\rm GR}(p^r,s)[G]$ are established. The analogous results for self-dual and complementary dual cyclic codes over Galois Rings are therefore obtained as corollaries.Comment: 22 page
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Self-dual and complementary dual abelian codes over Galois Rings
Jacodesmath Institute, 2019Co-Authors: Jitman Somphong, Ling SanAbstract:Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes over Galois Rings are studied in terms of the ideals in the group Ring ${ GR}(p^r,s)[G]$, where $G$ is a finite abelian group and ${ GR}(p^r,s)$ is a Galois Ring. Characterizations of self-dual abelian codes have been given together with necessary and sufficient conditions for the existence of a self-dual abelian code in ${ GR}(p^r,s)[G]$. A general formula for the number of such self-dual codes is established. In the case where $\gcd(|G|,p)=1$, the number of self-dual abelian codes in ${ GR}(p^r,s)[G]$ is completely and explicitly determined. Applying known results on cyclic codes of length $p^a$ over ${ GR}(p^2,s)$, an explicit formula for the number of self-dual abelian codes in ${ GR}(p^2,s)[G]$ are given, where the Sylow $p$-subgroup of $G$ is cyclic. Subsequently, the characterization and enumeration of complementary dual abelian codes in ${ GR}(p^r,s)[G]$ are established. The analogous results for self-dual and complementary dual cyclic codes over Galois Rings are therefore obtained as corollaries
