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 \(q=3\).