Distance-2 MDS Codes and Latin Colorings in the Doob Graphs
Sign Up to like & getrecommendations! Published in 2018 at "Graphs and Combinatorics"
DOI: 10.1007/s00373-018-1926-4
Abstract: The maximum independent sets in the Doob graphs D(m, n) are analogs of the distance-2 MDS codes in Hamming graphs and of the latin hypercubes. We prove the characterization of these sets stating that every such… read more here.
Keywords: mds codes; codes latin; doob graphs; distance mds ... See more keywords
On the Construction of Quantum MDS Codes
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DOI: 10.1007/s10773-018-3867-3
Abstract: Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. The paper is devoted to the construction of new quantum MDS codes based on classical constacyclic codes and cyclic codes over Fq2$\mathbb {F}_{q^{2}}$. We… read more here.
Keywords: mds codes; quantum mds; construction quantum; quantum ... See more keywords
Quantum MDS codes from BCH constacyclic codes
Sign Up to like & getrecommendations! Published in 2018 at "Quantum Information Processing"
DOI: 10.1007/s11128-018-2049-9
Abstract: One central theme in quantum error correction is to construct quantum codes that have large minimum distances. It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. Recently, some quantum MDS codes… read more here.
Keywords: mds codes; quantum mds; constacyclic codes; codes bch ... See more keywords
Some quantum MDS codes with large minimum distance from generalized Reed-Solomon codes
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DOI: 10.1007/s12095-017-0274-1
Abstract: Quantum maximum-distance-separable (MDS) codes are a significant class of quantum codes. In this paper, we mainly utilize classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct five new classes of quantum MDS codes with large minimum… read more here.
Keywords: mds codes; reed solomon; distance; generalized reed ... See more keywords
A Multistage Method for SCMA Codebook Design Based on MDS Codes
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DOI: 10.1109/lwc.2019.2925801
Abstract: Sparse code multiple access (SCMA) has been recently proposed for the future generation of wireless communication standards. SCMA system design involves specifying several parameters. To simplify the procedure, most works consider a multistage design approach.… read more here.
Keywords: scma; codebook design; scma codebook; mds codes ... See more keywords
Construction of MDS Codes With Complementary Duals
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DOI: 10.1109/tit.2016.2644660
Abstract: A linear complementary dual (LCD) code is a linear code with complimentary dual. LCD codes have been extensively studied in literature. On the other hand, maximum distance separable (MDS) codes are an important class of… read more here.
Keywords: mds codes; construction mds; codes complementary; mds ... See more keywords
New Constructions of MDS Codes With Complementary Duals
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2017.2748955
Abstract: Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in… read more here.
Keywords: mds codes; constructions mds; lcd codes; lcd mds ... See more keywords
Explicit MDS Codes With Complementary Duals
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2018.2816934
Abstract: In 1964, Massey introduced a class of codes with complementary duals which are called linear complimentary dual (LCD) codes. He showed that LCD codes have applications in communication system, side-channel attack and so on. LCD… read more here.
Keywords: mds codes; lcd codes; codes complementary; explicit mds ... See more keywords
Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2019.2950245
Abstract: In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls.… read more here.
Keywords: hermitian hulls; mds eaqeccs; euclidean hermitian; mds codes ... See more keywords
A Systematic Construction of MDS Codes With Small Sub-Packetization Level and Near-Optimal Repair Bandwidth
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DOI: 10.1109/tit.2020.3036386
Abstract: In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes… read more here.
Keywords: repair bandwidth; packetization level; sub packetization; mds codes ... See more keywords
Infinite Families of 3-Designs and 2-Designs From Almost MDS Codes
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2022.3157199
Abstract: Combinatorial designs are closely related to linear codes. Recently, some near MDS codes were employed to construct $t$ -designs by Ding and Tang, which settles the question as to whether there exists an infinite family… read more here.
Keywords: inline formula; mds codes; tex math;