A class of linear codes of length 2 over finite chain rings

Abstract

© 2020 World Scientific Publishing Company. Let pm be a finite field of cardinality pm, where p is an odd prime, k,λ be positive integers satisfying λ ≥ 2, and denote = pm[x]/(f(x)λpk), where f(x) is an irreducible polynomial in pm[x]. In this note, for any fixed invertible element ω ×, we present all distinct linear codes S over of length 2 satisfying the condition: (ωf(x)pka1,a0) S for all (a0,a1) S. This conclusion can be used to determine the structure of (δ + αu2)-constacyclic codes over the finite chain ring pm[u]/(u2λ) of length npk for any positive integer n satisfying gcd(p,n) = 1.