On Some Ternary LCD Codes

Nitin S. Darkunde; Arunkumar R. Patil

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arXiv · 1802.03014

On Some Ternary LCD Codes

Nitin S. Darkunde·Arunkumar R. Patil

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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 $q=3$.

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Nitin S. Darkunde, Arunkumar R. Patil. 2018-02-08. On Some Ternary LCD Codes. https://arxiv.org/abs/1802.03014

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