Minimum Distance Bounds for Linear Codes over $GF(7)$

Abstract

Let $[n,k,d;q]$-codes be linear codes of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q)$. Let $d_7(n,k)$ be the maximum possible minimum Hamming distance of a linear $[n,k,d;7]$-code for given values of $n$ and $k$. In this paper, fifty-eight new linear codes over $GF(7)$ are constructed, the nonexistence of sixteen linear codes is proved and a table of $d_7(n,k)$ , $k\le 7$, $n\le 100$ is presented.