On the Hamming Distances of Constacyclic Codes of Length 5pS
Hai Quang Dinh, Xiaoqiang Wang, Jirakom Sirisrisakulchai · IEEE Access · 2020
Let$p$be a prime,$s$,$m$be positive integers, and$\lambda $be a nonzero element of the finite field$\mathbb {F}_{p^{m}}$. In this paper, the algebraic structures of constacyclic codes of length$5~p^{s}~(p eq 5)$are obtained, which provide all self-dual, self-orthogonal and dual containing codes. Moreover, the exact values of the Hamming distances of all such codes are completely determined. Among other results, we obtain the degrees of the generator polynomials of all MDS repeated-root constacyclic codes of arbitrary length. As applications, several new and optimal codes are provided.