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

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 \(d_7(n,k)\) \, \(k\leq7\), \(n\leq100\) is presented.