On some ternary LCD codes

Abstract

The main aim of this paper is to study LCD codes. Linear codes with complementary dual (LCD) are those codes which have their intersection with their dual code as {0}. In this paper we will give rather alternative proof of Massey’s theorem [8], which is one of the most important characterization of LCD codes. Let LCD[n, k]3 denote the maximum of possible values of d among [n, k,d] ternary LCD codes. In [4], authors have given upper bound on LCD[n, k]2 and extended this result for LCD[n, k]q, for any q, where q is some prime power. We will discuss cases when this bound is attained for q = 3 and see some new constructions of LCD codes.