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 $q=3$.
Categories: cs.IT math.IT