Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

Abstract

Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring. In this paper, the symbol-pair distances of all γ-constacyclic codes of length ps over R are completely determined.

Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over Fq+uFq+u2Fq

“…Then, their Hamming distances have been computed by Dinh et al [22]. In [23], Charkani et al computed their symbol-pair distances.…”