New Optimal Ternary Linear Codes of Dimension $6$

Abstract

In this paper, new optimal $(pm,m)$ and $(pm,m-1)$ ternary linear codes of dimension 6 are presented. These codes belong to the class of quasi-twisted codes, and have been constructed using a greedy local search algorithm. Other codes are also given which provide a lower bound on the maximum possible minimum distance. The minimum distances of known quasi-twisted codes of dimension 6 are given.