Results 21 to 30 of about 35,611 (258)
Maximum Distance Separable Codes for Symbol-Pair Read Channels [PDF]
, 2013 We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed.
Chengmin Wang +5 more
core +1 more source
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
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
On Symbol-Pair Distance of a Class of Constacyclic Codes of Length 3ps over
Axioms, 2023 Let p≠3 be any prime. In this paper, we compute symbol-pair distance of all γ-constacyclic codes of length 3ps over the finite commutative chain ring R=Fpm+uFpm, where γ is a unit of R which is not a cube in Fpm.
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
Twisted Reed-Solomon Codes [PDF]
, 2017 We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are
Beelen, Peter +2 more
core +2 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
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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
Enumeration of Self-Dual Codes of Length 6 over ℤp
Mathematics, 2019 The purpose of this paper is to classify and enumerate self-dual codes of length 6 over finite field Z p .
Whan-Hyuk Choi
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