New Linear Codes of Dimensions \(5\) and \(6\) over \(GF(8)\)

Abstract

Let \([n, k, d; g]\)-codes be linear codes of length \(n\), dimension \(k\) and minimum Hamming distance \(d\) over \(\mathrm{GF}(g)\). Let \(d_8(n, k)\) be the maximum possible minimum Hamming distance of a linear \([n, k, d; 8]\)-code for given values of \(n\) and \(k\). In this paper, twenty-two new linear codes over \(\mathrm{GF}(8)\) are constructed which improve the bounds on \(d_8(n, k)\).