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Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices
Computational and Mathematical Methods, 2023 In this paper, we present an innovative approach for the discovery of involutory maximum distance separable (MDS) matrices over finite fields F2q, derived from MDS self-dual codes, by employing a technique based on genetic algorithms. The significance of
El Mehdi Bellfkih +4 more
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Complete Characterizations of Optimal Locally Repairable Codes With Locality 1 and
IEEE Access, 2019 A locally repairable code (LRC) is a [n, k, d] linear code with length n, dimension k, minimum distance d and locality r, which means that every code symbol can be repaired by at most r other symbols.
Yichong Xia, Bin Chen
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Long MDS Codes for Optimal Repair Bandwidth [PDF]
, 2012 MDS codes are erasure-correcting codes that can correct the maximum number of erasures given the number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in ...
Bruck, Jehoshua +2 more
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Improved Field Size Bounds for Higher Order MDS Codes [PDF]
International Symposium on Information Theory, 2022 Higher order MDS codes are an interesting generalization of MDS codes recently introduced by Brakensiek, Gopi and Makam (IEEE Trans. Inf. Theory 2022).
Joshua Brakensiek, Manik Dhar, S. Gopi
semanticscholar +1 more source
On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6
IEEE Access, 2020 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 ...
Hai Q. Dinh +2 more
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Constructions of near MDS codes which are optimal locally recoverable codes [PDF]
Finite Fields Their Appl., 2022 A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have nice applications
Xiaoru Li, Ziling Heng
semanticscholar +1 more source
Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
Cryptography, 2021 The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim ...
Johann-Philipp Thiers +1 more
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Near-MDS Codes from Maximal Arcs in PG$(2, q)$ [PDF]
Finite Fields Their Appl., 2022 The singleton defect of an $[n,k,d]$ linear code ${\cal C}$ is defined as $s({\cal C})=n-k+1-d$. Codes with $S({\cal C})=0$ are called maximum distance separable (MDS) codes, and codes with $S(\cal C)=S(\cal C ^{\bot})=1$ are called near maximum distance
Li Xu, Cuiling Fan, Dongchun Han
semanticscholar +1 more source
Access vs. Bandwidth in Codes for Storage [PDF]
, 2012 Maximum distance separable (MDS) codes are widely used in storage systems to protect against disk (node) failures. A node is said to have capacity $l$ over some field $\mathbb{F}$, if it can store that amount of symbols of the field.
Bruck, Jehoshua +2 more
core +3 more sources
On additive MDS codes with linear projections [PDF]
Finite Fields Their Appl., 2022 We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let $C$ be an $\mathbb F_q$-linear $(n,q^{hk},n-k+1)_{q^h}$ MDS code over $\mathbb F_{q^h}$.
S. Adriaensen, Simeon Ball
semanticscholar +1 more source