New quantum codes from constacyclic and additive constacyclic codes

Let p be a prime and q = p(r), for an integer r >= 1. This article studies lambda = (lambda(1) + u lambda(2)+ v lambda(3))-constacyclic codes of length n over a class of finite commutative non-chain rings R = F-q [u, v]/< u(2) - gamma u, v(2) - delta v, uv = vu = 0 >, where gamma, delta is an element of F-q*. First, we decompose (lambda(1)+u lambda(2)+ v lambda(3))-constacyclic code into the direct sum of lambda(1)-constacyclic, (lambda(1)+gamma lambda(2))-constacyclic and (lambda(1)+delta lambda(3))-constacyclic codes over F-q, respectively. Then, we determine the necessary and sufficient condition for these codes to contain their Euclidean duals. Further, we extend the study to F-q R-additive lambda-constacyclic codes of length (n, m) which are R[x]-submodules of S-n,S- m = F-q [x]/< x(n)-1 > xR[x]/< x(m) -lambda >. Apart from other results, we also discuss the dual-containing separable Fq R-additive lambda-constacyclic codes. Finally, by using the CSS construction on the Gray images of these codes, we obtainmany new and better quantum codes that improve on the known existing quantum codes available in recent articles.