Results 11 to 20 of about 35,611 (258)
Application of Constacyclic codes to Quantum MDS Codes [PDF]
IEEE Transactions on Information Theory, 2014 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 ...
Chen, Bocong, Ling, San, Zhang, Guanghui
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Filomat, 2018 Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and detecting ...
Koroglu, Mehmet E., Sarı, Mustafa
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The Weights in MDS Codes [PDF]
IEEE Transactions on Information Theory, 2010 The weights in MDS codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n-k+1 to n. The
Ezerman, Martianus Frederic +2 more
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Partial MDS Codes With Regeneration [PDF]
IEEE Transactions on Information Theory, 2021 Extended version of arXiv:2001 ...
Lukas Holzbaur +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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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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Group codes over symmetric groups
AIMS Mathematics, 2023 Let $ \Bbb F_{q} $ be a finite field of characteristic $ q $ and $ S_n $ a symmetric group of order $ n! $. In this paper, group codes in the symmetric group algebras $ \Bbb F_{q}S_n $ with $ q > 3 $ and $ n = 3, 4 $ are proposed.
Yanyan Gao , Yangjiang Wei
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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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Systematic MDS erasure codes based on vandermonde matrices [PDF]
, 2004 An increasing number of applications in computer communications uses erasure codes to cope with packet losses. Systematic maximum-distance separable (MDS) codes are often the best adapted codes.
Fimes, Jérôme, Lacan, Jérôme
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