New Quasi-Cyclic Codes over \(GF(8)\) with Improved Minimum Distances

Abstract

One of the most important problems of coding theory is to construct codes with the best possible minimum distance. The class of quasi-cyclic codes has proved to be a good source for such codes. In this paper, we use the algebraic structure of quasi-cyclic codes and the BCH type bound introduced in [17] to search for quasi-cyclic codes which improve the minimum distances of the best-known linear codes. We construct \(11\) new linear codes over \(\text{GF}(8)\) where \(3\) of these codes are one unit away from being optimal.