On constacyclic codes of length ps over Fpm[u, v]/⟨u2, v2, uv - vu⟩

Let p be a prime number, in this paper, we investigate the structures of all constacyclic codes of length p(s) over the ring R-u2,R-v2,R-pm = F-pm[u, v]/< u(2), v(2), uv - vu). The units of the ring R-u2,R-v2,R-pm can be divided into following five forms: alpha, lambda(1) = alpha + delta(1)uv, lambda(2) =alpha + gamma v +delta uv, lambda(3)= alpha + beta u+delta uv, lambda(4) = alpha+beta u+gamma v+delta uv, where alpha, beta, gamma, delta(1) is an element of F-pm* and delta is an element of F-pm. We obtain the algebraic structures of all constacyclic codes of length p(s) over R-u2 ,R-v2,R- pm except (alpha + delta(1)uv)-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 lambda(2), lambda(3) and lambda(4) are determined. We also provide examples to illustrate our results, which include several optimal codes. (C) 2020 Elsevier B.V. All rights reserved.