MDS symbol-pair repeated-root constacylic codes of prime power lengths over F<inf>q</inf>+ uF<inf>q</inf>+ u²F<inf>q</inf>

Abstract

MDS symbol-pair codes forms an optimal class of symbol-pair codes for their best error-correction capability. ψ-constacyclic codes of length ps over R=Fq+uFq+u2Fq(u3=0), where q= pm, ψ is a nonzero element of Fq, are precisely the ideals of the ring R[x]/⟨xps-ψ⟩ which is a local finite non chain ring with the non principal maximal ideal ⟨ u, x- φ⟩ , where φ∈ Fq satisfying ψ=φps. In this paper, all MDS symbol-pair ψ-constacyclic codes of length ps over R are established.