Results 21 to 30 of about 9,399 (155)

New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields

Entropy, 2019
Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality.
Aixian Zhang, Zhe Ji
doaj   +1 more source

On Symbol-Pair Distance of a Class of Constacyclic Codes of Length 3p^s over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$

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, Hiep L. Thi, Roengchai Tansuchat   +2 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, Jürgen Freudenberger   +1 more
doaj   +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, Said Nouh, Imrane Chems Eddine Idrissi, Khalid Louartiti, Jamal Mouline   +4 more
doaj   +1 more source

Constructions of quantum MDS codes [PDF]

Quantum Information Processing, 2021
10 pages,2 ...
Hualu Liu, Xiusheng Liu
openaire   +2 more sources

Infinite families of MDS and almost MDS codes from BCH codes

CoRR, 2023
In this paper, the sufficient and necessary condition for the minimum distance of the BCH codes over $\mathbb{F}_q$ with length $q+1$ and designed distance 3 to be 3 and 4 are provided. Let $d$ be the minimum distance of the BCH code $\mathcal{C}_{(q,q+1,3,h)}$. We prove that (1) for any $q$, $d=3$ if and only if $\gcd(2h+1,q+1)>1$; (2) for $q$ odd,
Haojie Xu, Xia Wu 0002, Wei Lu 0022, Xiwang Cao   +3 more
openaire   +2 more sources

Strongly-MDS convolutional codes [PDF]

IEEE Transactions on Information Theory, 2006
33 ...
Heide Gluesing-Luerssen, Joachim Rosenthal, Roxana Smarandache   +2 more
openaire   +3 more sources

Application of Constacyclic Codes to Quantum MDS Codes [PDF]

IEEE Transactions on Information Theory, 2015
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction and the quantum Singleton bound. If $C^{\perp_{H}}\subseteq C$, we say that $C$ is a dual-containing
Bocong Chen, San Ling, Guanghui Zhang
openaire   +3 more sources

Enumeration of Self-Dual Codes of Length 6 over ℤ_p

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

MDS codes in Doob graphs [PDF]

Problems of Information Transmission, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Evgeny Bespalov, Denis S. Krotov
openaire   +3 more sources