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On the Hamming Distances of Constacyclic Codes of Length 5pS

Authors: 

Hai Q. Dinh, Xiaoqiang Wang, Jirakom Sirisrisakulchai

Source title: 
IEEE Access, 8: 46242-46254, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

Let p be a prime, s, m be positive integers, and λ be a nonzero element of the finite field Fp(m). In this paper, the algebraic structures of constacyclic codes of length 5ps (p ≠ 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.