Hamming distances of constacyclic codes of length \(3p^s\) and optimal codes with respect to the Griesmer and Singleton bounds (Q1995224)

In this paper, the authors complete the problem of determining minimum distances of all the repeated-root constacyclic codes of length \(3p^s,\ p\ne 3,\) over the finite field \(\mathbb{F}_{p^m}\). Moreover they describe all such codes that are optimal with respect to the Griesmer bound and the Singleton bound. The proofs are based on the general relation between minimum distances of single-root constacyclic codes and repeated-root constacyclic codes. Namely, the authors obtain that the minimum distance of a repeated-root constacyclic code of length \(lp^s\) can be determined by the minimum distance of the simple-root constacyclic codes of length \(l\).