Results 11 to 20 of about 63,034 (284)
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
doaj +1 more source
Asymptotically MDS Array BP-XOR Codes [PDF]
, 2017 Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process.
Arslan, Suayb S.
core +2 more sources
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
doaj +1 more source
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
core +3 more sources
The Weights in MDS Codes [PDF]
IEEE Transactions on Information Theory, 2011 5 pages, submitted to IEEE Trans. IT. This version 2 is the revised version after the refereeing process.
Ezerman, M.F., Grassl, M., Sole, P.
openaire +4 more sources
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
doaj +1 more source
Application of Classical Hermitian Self-Orthogonal MDS Codes to Quantum MDS Codes [PDF]
IEEE Transactions on Information Theory, 2010 In this paper, we first construct several classes of classical Hermitian self-orthogonal maximum distance separable (MDS) codes. Through these classical codes, we are able to obtain various quantum MDS codes. It turns out that many of our quantum codes are new in the sense that the parameters of our quantum codes cannot be obtained from all previous ...
Jin, Lingfei +3 more
openaire +3 more sources
Some subfield codes from MDS codes
Advances in Mathematics of Communications, 2023 The authors give a construction of subfield codes from a family of MDS codes by using group characters and trace representations. In Subsection 2.3 the construction of the investigated subfield codes is explained. (This construction itself is actually due to \textit{C. Ding} and \textit{Z. Heng} [IEEE Trans. Inf. Theory 65, No. 8, 4715--4729 (2019; Zbl
Xiang, Can, Luo, Jinquan
openaire +2 more sources
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
doaj +1 more source
Partial MDS Codes with Local Regeneration
, 2020 Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code.
Holzbaur, Lukas +3 more
core +1 more source