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A Family of Codes With Locality Containing Optimal Codes
IEEE Access, 2022 Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes.
Bruno Andrade +3 more
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Enumeration of Optimal Equidistant Codes
Mathematics, 2022 Problems of search and enumeration of binary and ternary equidistant codes are considered in the paper. We investigate some combinatorial algorithms and develop specialized computer packages to find non-equivalent optimal binary and ternary equidistant ...
Galina Bogdanova, Todor Todorov
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Two Families of Optimal Ternary Cyclic Codes With Two Zeros
IEEE Access, 2022 Cyclic codes are an important subclass of linear codes and have wide applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms.
Jinmei Fan, Binseng Wang
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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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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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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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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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ON OPTIMAL QUANTUM CODES [PDF]
International Journal of Quantum Information, 2004 We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters 〚n, n - 2d + 2, d〛q exist for all 3≤n≤q and 1≤d≤n/2+1.
Grassl, M., Beth, T., Rötteler, M.
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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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