New Quasi-Cyclic Degenerate Linear Codes over $GF(8)$

Let $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$, and minimum Hamming distance $d$ over $GF(q)$. One of the most important problems in coding theory is to construct codes with best possible minimum distances. Recently, quasi-cyclic (QC) codes were proved to contain many such codes. In this paper, twenty-five new codes over $GF(8)$ are constructed, which improve the best known lower bounds on minimum distance.