Abstract
Due to their important applications in theory and practice, linear complementary dual (LCD) codes and self-orthogonal codes have received much attention in the last decade. The objective of this paper is to extend a recent construction of binary LCD codes and self-orthogonal codes to the general $ p $-ary case, where $ p $ is an odd prime. Based on the extended construction, several classes of $ p $-ary linear codes are obtained. The characterizations of these linear codes to be LCD or self-orthogonal are derived. The duals of these linear codes are also studied. It turns out that the proposed linear codes are optimal in many cases in the sense that their parameters meet certain bounds on linear codes. The weight distributions of these linear codes are settled.
Highlights
Let q be a power of a prime and Fq be the finite field with q elements
Very recently, employing a generic construction of linear codes by Ding [12], Zhou el al. [36] obtained several class of linear complementary dual (LCD) codes and self-orthogonal codes which are optimal in many cases in the sense that their parameters meets certain bounds on linear codes
The main objective of this paper is to extend the construction of LCD codes and self-orthogonal codes in [36] from binary case to the general p-ary case, where p is an odd prime
Summary
Let q be a power of a prime and Fq be the finite field with q elements. Let Fnq denote the vector space over Fq with dimension n. Key words and phrases: Linear codes, self-orthogonal codes, LCD codes, weight distributions, Krawtchouck polynomial. [36] obtained several class of LCD codes and self-orthogonal codes which are optimal in many cases in the sense that their parameters meets certain bounds on linear codes. The main objective of this paper is to extend the construction of LCD codes and self-orthogonal codes in [36] from binary case to the general p-ary case, where p is an odd prime. People can only determine the weight distribution of a few class of self-orthogonal codes. We completely determine the weight distributions of the linear codes constructed in this paper. Many LCD codes and self-orthogonal codes presented in this paper are optimal or almost optimal in the sense that they meet certain bounds on general linear codes. We will compare some of the codes presented in this paper with the tables of best known linear codes (referred to as the Database later) maintained by Markus Grassl at http://www.codetables.de
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