New ternary quasi-cyclic codes with improved minimum distances

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One of the most important problems of coding theory is to construct codes with best possible minimum distances. In this paper, we use the algebraic structure of quasi-cyclic codes and the BCH type bound on the minimum distance to search for quasicyclic codes over 5, the finite field with five elements, which improve the minimum distances of best-known linear codes. We construct 15 new linear codes of this type.