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Tania Sidana - One of the best experts on this subject based on the ideXlab platform.
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On $b$ -Symbol Distances of Repeated-Root Constacyclic Codes
IEEE Transactions on Information Theory, 2019Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let $p$ be a prime, $s$ be a positive integer, and let $b$ be an integer satisfying $2 \leq b . In this paper, we obtain $b$ -symbol distances of all Repeated-Root constacyclic codes of length $p^{s}$ over finite fields. Using this result, we determine $b$ -symbol distances of all Repeated-Root constacyclic codes of length $p^{s}$ over finite commutative chain rings. We also list all MDS $b$ -symbol Repeated-Root constacyclic codes of length $p^{s}$ over finite fields, and all MDS $b$ -symbol Repeated-Root constacyclic codes of length $p^{s}$ over finite commutative chain rings in general.
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Repeated-Root constacyclic codes of arbitrary lengths over the Galois ring GR(p2,m)
Discrete Mathematics Algorithms and Applications, 2018Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let p be a prime, m be a positive integer, and let GR(p2,m) be the Galois ring of characteristic p2 and cardinality p2m. In this paper, all Repeated-Root constacyclic codes of arbitrary lengths ove...
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Repeated-Root constacyclic codes of arbitrary lengths over the Galois ring GR(p2,m)
Discrete Mathematics Algorithms and Applications, 2018Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let [Formula: see text] be a prime, [Formula: see text] be a positive integer, and let GR[Formula: see text] be the Galois ring of characteristic [Formula: see text] and cardinality [Formula: see text]. In this paper, all Repeated-Root constacyclic codes of arbitrary lengths over GR[Formula: see text] their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over GR[Formula: see text] are also listed. To illustrate the results, all cyclic and negacyclic codes of length 10 over [Formula: see text] are obtained.
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Repeated-Root constacyclic codes over finite commutative chain rings and their distances
2017Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let $\mathcal{R}_e$ be a finite commutative chain ring with nilpotency index $e \geq 2.$ In this paper, all Repeated-Root constacyclic codes of arbitrary lengths over $\mathcal{R}_{2},$ their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over $\mathcal{R}_{2}$ are also listed. Moreover, Hamming distances, Rosenbloom-Tsfasman distances and Rosenbloom-Tsfasman weight distributions of all Repeated-Root constacyclic codes over $\mathcal{R}_{2}$ and some Repeated-Root constacyclic codes over $\mathcal{R}_{e}$ are determined.
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Repeated-Root constacyclic codes over the finite chain ring $\mathbf{ \mathbb{F}_{p^m}[u]/\langle u^3 \rangle }$
arXiv: Number Theory, 2017Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let $\mathcal{R}=\mathbb{F}_{p^m}[u]/\langle u^3 \rangle $ be the finite commutative chain ring with unity, where $p$ is a prime, $m$ is a positive integer and $\mathbb{F}_{p^m}$ is the finite field with $p^m$ elements. In this paper, we determine all Repeated-Root constacyclic codes of arbitrary lengths over $\mathcal{R},$ their sizes and their dual codes. As an application, we list some isodual constacyclic codes over $\mathcal{R}.$ We also determine Hamming distances, RT distances, and RT weight distributions of some Repeated-Root constacyclic codes over $\mathcal{R}.$
Hai Q. Dinh - One of the best experts on this subject based on the ideXlab platform.
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hamming distance of Repeated Root constacyclic codes of length 2p s over mathbb f _ p m u mathbb f _ p m
Applicable Algebra in Engineering Communication and Computing, 2020Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Atul Gaur, Indivar Gupta, Manoj Kumar Singh, Roengchai TansuchatAbstract:Let p be an odd prime, and $$\delta$$ be an arbitrary unit of the finite chain ring $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)$$. The Hamming distances of all $$\delta$$-constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS Repeated-Root $$\delta$$-constacyclic codes of length $$2p^s$$ over $$\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}$$.
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Hamming distance of Repeated-Root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$
Applicable Algebra in Engineering Communication and Computing, 2020Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Atul Gaur, Indivar Gupta, Manoj Kumar Singh, Roengchai TansuchatAbstract:Let p be an odd prime, and $$\delta$$ be an arbitrary unit of the finite chain ring $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)$$. The Hamming distances of all $$\delta$$-constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS Repeated-Root $$\delta$$-constacyclic codes of length $$2p^s$$ over $$\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}$$.
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Hamming distance of Repeated-Root constacyclic codes of length $$2p^s$$2ps over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$Fpm+uFpm
Applicable Algebra in Engineering Communication and Computing, 2020Co-Authors: Hai Q. Dinh, Atul Gaur, Indivar Gupta, Manoj Kumar Singh, Abhay K. Singh, Roengchai TansuchatAbstract:Let p be an odd prime, and $$\delta$$ δ be an arbitrary unit of the finite chain ring $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)$$ F p m + u F p m ( u 2 = 0 ) . The Hamming distances of all $$\delta$$ δ -constacyclic codes of length $$2p^s$$ 2 p s over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ F p m + u F p m are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS Repeated-Root $$\delta$$ δ -constacyclic codes of length $$2p^s$$ 2 p s over $$\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}$$ F p m + u F p m .
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On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6 p s
IEEE Access, 2020Co-Authors: Hai Q. Dinh, Xiaoqiang Wang, Paravee ManeejukAbstract:Let $p$ be an odd prime, $s$ , $m$ be positive integers such that $p^{m}\equiv 2 \pmod 3$ . In this paper, using the relationship about Hamming distances between simple-Root cyclic codes and Repeated-Root cyclic codes, the Hamming distance of all cyclic codes of length $6p^{s}$ over finite field $\mathbb F_{p^{m}}$ is obtained. All maximum distance separable (MDS) cyclic codes of length $6p^{s}$ are established.
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Repeated-Root constacyclic codes of length $ 3\ell^mp^s $
Advances in Mathematics of Communications, 2020Co-Authors: Yan Liu, Hai Q. Dinh, Minjia Shi, Songsak SriboonchittaAbstract:Let \begin{document}$ p $\end{document} be a prime different from 3, and \begin{document}$ \ell $\end{document} be an odd prime different from 3 and \begin{document}$ p $\end{document} . In terms of generator polynomials, structures of constacyclic codes and their duals of length \begin{document}$ 3\ell^mp^s $\end{document} over \begin{document}$ \mathbb{F}_q $\end{document} are established, where \begin{document}$ q $\end{document} is a power of \begin{document}$ p $\end{document} . We discuss the enumeration of all cyclic codes of length \begin{document}$ 3\cdot2^s\ell^m $\end{document} , that generalizes the construction of [ 15 ] (2016), which is the special case of \begin{document}$ m = 1 $\end{document} . In addition, as an application, the characterization and enumeration of all linear complementary dual cyclic codes of length \begin{document}$ 6\ell^mp^s $\end{document} over \begin{document}$ \mathbb{F}_q $\end{document} are obtained.
Anuradha Sharma - One of the best experts on this subject based on the ideXlab platform.
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On $b$ -Symbol Distances of Repeated-Root Constacyclic Codes
IEEE Transactions on Information Theory, 2019Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let $p$ be a prime, $s$ be a positive integer, and let $b$ be an integer satisfying $2 \leq b . In this paper, we obtain $b$ -symbol distances of all Repeated-Root constacyclic codes of length $p^{s}$ over finite fields. Using this result, we determine $b$ -symbol distances of all Repeated-Root constacyclic codes of length $p^{s}$ over finite commutative chain rings. We also list all MDS $b$ -symbol Repeated-Root constacyclic codes of length $p^{s}$ over finite fields, and all MDS $b$ -symbol Repeated-Root constacyclic codes of length $p^{s}$ over finite commutative chain rings in general.
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Repeated-Root constacyclic codes of arbitrary lengths over the Galois ring GR(p2,m)
Discrete Mathematics Algorithms and Applications, 2018Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let p be a prime, m be a positive integer, and let GR(p2,m) be the Galois ring of characteristic p2 and cardinality p2m. In this paper, all Repeated-Root constacyclic codes of arbitrary lengths ove...
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Repeated-Root constacyclic codes of arbitrary lengths over the Galois ring GR(p2,m)
Discrete Mathematics Algorithms and Applications, 2018Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let [Formula: see text] be a prime, [Formula: see text] be a positive integer, and let GR[Formula: see text] be the Galois ring of characteristic [Formula: see text] and cardinality [Formula: see text]. In this paper, all Repeated-Root constacyclic codes of arbitrary lengths over GR[Formula: see text] their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over GR[Formula: see text] are also listed. To illustrate the results, all cyclic and negacyclic codes of length 10 over [Formula: see text] are obtained.
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Repeated-Root constacyclic codes over finite commutative chain rings and their distances
2017Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let $\mathcal{R}_e$ be a finite commutative chain ring with nilpotency index $e \geq 2.$ In this paper, all Repeated-Root constacyclic codes of arbitrary lengths over $\mathcal{R}_{2},$ their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over $\mathcal{R}_{2}$ are also listed. Moreover, Hamming distances, Rosenbloom-Tsfasman distances and Rosenbloom-Tsfasman weight distributions of all Repeated-Root constacyclic codes over $\mathcal{R}_{2}$ and some Repeated-Root constacyclic codes over $\mathcal{R}_{e}$ are determined.
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Repeated-Root constacyclic codes over the finite chain ring $\mathbf{ \mathbb{F}_{p^m}[u]/\langle u^3 \rangle }$
arXiv: Number Theory, 2017Co-Authors: Anuradha Sharma, Tania SidanaAbstract:Let $\mathcal{R}=\mathbb{F}_{p^m}[u]/\langle u^3 \rangle $ be the finite commutative chain ring with unity, where $p$ is a prime, $m$ is a positive integer and $\mathbb{F}_{p^m}$ is the finite field with $p^m$ elements. In this paper, we determine all Repeated-Root constacyclic codes of arbitrary lengths over $\mathcal{R},$ their sizes and their dual codes. As an application, we list some isodual constacyclic codes over $\mathcal{R}.$ We also determine Hamming distances, RT distances, and RT weight distributions of some Repeated-Root constacyclic codes over $\mathcal{R}.$
Shixin Zhu - One of the best experts on this subject based on the ideXlab platform.
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Repeated-Root constacyclic codes of length \begin{document}$ 6lp^s $\end{document}
Advances in Mathematics of Communications, 2021Co-Authors: Li Liu, Shixin ZhuAbstract:Let \begin{document}$ \mathbb{F}_{q} $\end{document} be a finite field with character \begin{document}$ p $\end{document} and \begin{document}$ p\neq{3},l\neq{3} $\end{document} be different odd primes. In this paper, we study constacyclic codes of length \begin{document}$ 6lp^s $\end{document} over finite field \begin{document}$ \mathbb{F}_{q} $\end{document} . The generator polynomials of all constacyclic codes and their duals are obtained. Moreover, we give the characterization and enumeration of linear complementary dual (LCD) and self-dual constacyclic codes of length \begin{document}$ 6lp^s $\end{document} over \begin{document}$ \mathbb{F}_{q} $\end{document} .
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New MDS Symbol-Pair Codes From Repeated-Root Codes
IEEE Communications Letters, 2018Co-Authors: Xiaoshan Kai, Shixin Zhu, Yusen Zhao, Huarong Luo, Zhe ChenAbstract:Symbol-pair codes can be used to guard against pair errors over symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pair-error correcting performance. In this letter, we construct three new MDS symbol-pair codes with minimum pair-distance six or seven through Repeated-Root constacyclic codes. In contrast with classical MDS codes, they have relatively large length.
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Repeated-Root constacyclic codes over F2+uF2+vF2+uvF2
Journal of Pure and Applied Algebra, 2018Co-Authors: Liqi Wang, Shixin ZhuAbstract:Abstract In this paper, we give the structures of all ( 1 + u + v ) -constacyclic codes of length 2 s over F 2 + u F 2 + v F 2 + u v F 2 , we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacyclic codes of length 2, 4 and 8.
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Repeated Root constacyclic codes over f2 uf2 vf2 uvf2
Journal of Pure and Applied Algebra, 2017Co-Authors: Liqi Wang, Shixin ZhuAbstract:Abstract In this paper, we give the structures of all ( 1 + u + v ) -constacyclic codes of length 2 s over F 2 + u F 2 + v F 2 + u v F 2 , we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacyclic codes of length 2, 4 and 8.
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On LCD Repeated-Root cyclic codes over finite fields
Journal of Applied Mathematics and Computing, 2017Co-Authors: Binbin Pang, Shixin ZhuAbstract:In this paper, we investigate the LCD Repeated-Root cyclic codes of length \(n=n'p^r\) over the finite field \(\mathbb {F}_q\), where gcd\((n',p)=1\). We give a necessary and sufficient condition for a Repeated-Root cyclic code to be LCD over \(\mathbb {F}_q\). We also determine the minimum distance of LCD Repeated-Root cyclic codes over \(\mathbb {F}_q\). Finally, we give the enumeration of LCD Repeated-Root cyclic codes of length n over \(\mathbb {F}_q\).
Lan Luo - One of the best experts on this subject based on the ideXlab platform.
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Non-Binary Quantum Synchronizable Codes From Repeated-Root Cyclic Codes
IEEE Transactions on Information Theory, 2018Co-Authors: Lan LuoAbstract:In this paper, we construct a new family of quantum synchronizable codes from Repeated-Root cyclic codes of lengths $p^{s}$ and $lp^{s}$ over $\mathbb {F}_{q}$ , where $s\geq 1~and l\geq 2$ are integers, and $p\geq 3$ is the odd characteristic. Within some loose limitations, these synchronizable codes can possess the best possible capability in synchronization recovery, and therefore, enriches the variety of good quantum synchronizable codes. Furthermore, by using known techniques in classical coding theory which convert the computation of the minimum distance of a Repeated-Root cyclic code to that of a shorter simple-Root cyclic code, we prove that the Repeated-Root cyclic codes of lengths $p^{s}$ and $lp^{s}$ are in general better than narrow-sense BCH codes of close lengths in terms of minimum distances, and thereby enable the obtained synchronizable codes to correct more Pauli errors.