On constacyclic codes of length p^s over F<inf>p^m</inf>[u,v]∕〈u²,v²,uv−vu〉

Abstract

© 2020 Elsevier B.V. Let p be a prime number, in this paper, we investigate the structures of all constacyclic codes of length ps over the ring Ru2,v2,pm=Fpm[u,v]∕〈u2,v2,uv−vu〉. The units of the ring Ru2,v2,pm can be divided into following five forms: α, λ1=α+δ1uv, λ2=α+γv+δuv, λ3=α+βu+δuv, λ4=α+βu+γv+δuv, where α,β,γ,δ1∈Fpm∗ and δ∈Fpm. We obtain the algebraic structures of all constacyclic codes of length ps over Ru2,v2,pm, except (α+δ1uv)-constacyclic codes, in terms of their polynomial generators and also find the number of codewords in each of these constacyclic codes. The number of constacyclic codes and duals of constacyclic codes corresponding to the units λ2,λ3 and λ4 are determined. We also provide examples to illustrate our results, which include several optimal codes.