Quantum Codes Obtained from Skew ϱ - λ -Constacyclic Codes over R k

Abstract

Let R k = F q u 1 , u 2 , ⋯ , u k / < u i 2 = α i u i , u i u j = u j u i = 0 > , where q = p m , p is an odd prime, α i is a unit over F q , and i , j = 1,2 , ⋯ , k . In this article, we define a Gray map from R k n to F q k + 1 n , we study the structure of skew ϱ - λ -constacyclic codes over R k , and then we give the necessary and sufficient conditions for skew ϱ - λ -constacyclic codes over R k to satisfy dual containing. Further, we have obtained some new nonbinary quantum codes from skew ϱ - λ -constacyclic over R k by using the CSS construction.