Filomat 2019 Volume 33, Issue 1, Pages: 1-12
https://doi.org/10.2298/FIL1901001K
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On MDS negacyclic LCD codes
Koroglu Mehmet E. (Yıldız Technical University, Department of Mathematics, Faculty of Art and Sciences, Istanbul, Turkey)
Sarı Mustafa (Yıldız Technical University, Department of Mathematics, Faculty of Art and Sciences, Istanbul, Turkey)
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 capabilities for fixed length and dimension. The
construction of linear codes that are both LCD and MDS is a hard task in
coding theory. In this paper, we study the constructions of LCD codes that
are MDS from negacyclic codes over finite fields of odd prime power q
elements. We construct four families of MDS negacyclic LCD codes of length
n|q-1/2, n|q+1/2 and a family of negacyclic LCD codes of length n = q -
1. Furthermore, we obtain five families of q2-ary Hermitian MDS negacyclic
LCD codes of length n|(q-1) and four families of Hermitian negacyclic
LCD codes of length n = q2 + 1. For both Euclidean and Hermitian cases the
dimensions of these codes are determined and for some classes the minimum
distances are settled. For the other cases, by studying q and q2-cyclotomic
classes we give lower bounds on the minimum distance.
Keywords: linear codes, negacyclic codes, LCD codes, Euclidean inner product, Hermitian inner product