منابع مشابه
On MDS Negacyclic LCD Codes
This paper is devoted to the study of linear codes with complementary-duals (LCD) arising from negacyclic codes over finite fields Fq, where q is an odd prime power. We obtain two classes of MDS negacyclic LCD codes of length n| q−1 2 , n| q+1 2 and a class of negacyclic LCD codes of length n = q+1. Also, we drive some parameters of Hermitian negacyclic LCD codes over Fq2 of length n = q − 1 an...
متن کاملEuclidean and Hermitian LCD MDS codes
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Non-binary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. On the other hand, being optimal codes, maxim...
متن کاملCyclic arcs and pseudo-cyclic MDS codes
Cyclic arcs (defined by Storme and Van Maldghem, [1994]) and pseudocyclic MDS codes are equivalent objects. We survey known results on the existence of cyclic arcs. Some new results on cyclic arcs in PG(2, q) are also given.
متن کاملGradient Coding from Cyclic MDS Codes and Expander Graphs
Gradient Descent, and its variants, are a popular method for solving empirical risk minimization problems in machine learning. However, if the size of the training set is large, a computational bottleneck is the computation of the gradient, and hence, it is common to distribute the training set among worker nodes. Doing this in a synchronous fashion faces yet another challenge of stragglers (i....
متن کاملOn Hermitian LCD codes from cyclic codes and their applications to orthogonal direct sum masking
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. It was proved that asymptotically good Hermitian LCD codes exist. The objective of this paper is to construct some cyclic Hermitian LCD codes over finite fields and analyse their parameters. The dimensions of these codes ar...
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ژورنال
عنوان ژورنال: Procedia Computer Science
سال: 2019
ISSN: 1877-0509
DOI: 10.1016/j.procs.2019.06.104