On Some Ternary LCD Codes

Abstract

The main aim of this paper is to study $LCD$ codes. Linear code 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\cite{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 \cite{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 $q=3$.

Corrected typos from earlier version. arXiv admin note: substantial text overlap with arXiv:1801.05271