On the Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths

Abstract

© 1963-2012 IEEE. Let p be a prime, and λ be a nonzero element of the finite field Fpm. The λ-constacyclic codes of length psover Fpmare linearly ordered under set-theoretic inclusion, i.e., they are the ideals (x-λ0)i, 0 ≤ i ≤ psof the chain ring [(Fpm[x])/(xps-λ)]. This structure is used to establish the symbol-pair distances of all such λ-constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length p^{s} are obtained.