Hamming and Symbol-Pair Distances of Repeated-Root Constacyclic Codes of Prime Power Lengths over Fpm + uFpm

Abstract

IEEE The ring R = Fpm + uFpm has precisely pm(pm–1) units, which are of the forms γ and α+uβ, where 0 ≠ α,β,γ ∈ Fpm. Using generator polynomial structures of constacyclic codes of length ps over R, the Hamming and symbol-pair distance distributions of all such codes are completely determined. As examples, we provide some good codes with better parameters than the known ones.