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
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SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES [PDF]
Journal of Algebraic Systems, 2020 Let $mathbb{Z}_p$ be the finite field of integers modulo $p$, where $p>3$ is a prime integer. This paper presents new constructions of linear codes over $mathbb{Z}_p$.
A. Rafieepour, M. Mazrooei
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Exploring new lengths for q-ary quantum MDS codes with larger distance [PDF]
PLoS ONEXianmang He +3 more
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Strongly-MDS convolutional codes [PDF]
IEEE Transactions on Information Theory, 2006 33 ...
Gluesing-Luerssen, H +2 more
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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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On the Existence of XOR-Based Codes for Private Information Retrieval with Private Side Information
Entropy, 2021 We consider the problem of Private Information Retrieval with Private Side Information (PIR-PSI), wherein the privacy of the demand and the side information are jointly preserved. Although the capacity of the PIR-PSI setting is known, we observe that the
Murali Krishnan K. H., Jagadeesh Harshan
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Quantum MDS and Synchronizable Codes From Cyclic and Negacyclic Codes of Length 2
IEEE Access, 2020 Let p be an odd prime, and Fp(m) is the finite field of pm elements. In this paper, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length 2ps over Fp(m) are established.
Hai Q. Dinh +2 more
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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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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
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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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