Results 11 to 20 of about 7,804,605 (312)
Hamming Distance of Constacyclic Codes of Length
IEEE Access, 2021 Let $p$ be any prime, $s$ and $m$ be positive integers. In this paper, we completely determine the Hamming distance of all constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb {F}_{p^m}+ u\mathbb {F}_{p^m} + u^{2 ...
Hai Q. Dinh +3 more
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Self-Dual Codes, Symmetric Matrices, and Eigenvectors
IEEE Access, 2021 We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ using symmetric matrices and eigenvectors from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$ . Using this method, which is called a
Jon-Lark Kim, Whan-Hyuk Choi
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Some Results on Self-Complementary Linear Codes
Mathematics, 2023 Binary codes have a special place in coding theory since they are one of the most commonly used in practice. There are classes of codes specific only to the binary case. One such class is self-complementary codes.
Maria Pashinska-Gadzheva +2 more
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CoRR, 2021 This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords. Therefore, by replacing the new codewords, the binary data becomes another binary data regarding the intended goals.
Parviz Gharehbagheri +3 more
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Repeated-Root Constacyclic Codes Over the Chain Ring Fpm[u]/⟨u3⟩
IEEE Access, 2020 Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
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Asymptotically Optimal Codes Correcting Fixed-Length Duplication Errors in DNA Storage Systems [PDF]
IEEE Communications Letters, 2018 A (tandem) duplication of length ${k} $ is an insertion of an exact copy of a substring of length ${k} $ next to its original position.
Mladen Kovačević, V. Tan
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New Constructions of Optimal Locally Repairable Codes With Super-Linear Length [PDF]
IEEE Transactions on Information Theory, 2020 As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research.
Xiangliang Kong, Xin Wang, G. Ge
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On Optimal Locally Repairable Codes and Generalized Sector-Disk Codes [PDF]
International Symposium on Information Theory, 2020 Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper.
Han Cai, Moshe Schwartz
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Optimal Narain CFTs from codes
Journal of High Energy Physics, 2022 Recently established connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints by reducing them to algebraic identities.
Nikolaos Angelinos +2 more
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BVPs Codes for Solving Optimal Control Problems
Mathematics, 2021 Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontryagin’s minimum principle that generates Hamiltonian Boundary Value ...
Francesca Mazzia, Giuseppina Settanni
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