(xn-(a+bw),ξ,η)-skew constacyclic codes over Fq+wFq and their applications in quantum codes

Let p be an odd prime and m a positive integer such that q = p 2 m . First, we give the algebraic structure of ( x n - a , ξ , η ) -skew constacyclic codes and their Hermitian dual codes over F q , where ξ is an automorphism and η a ξ -derivation of F q , a is a unit of F q and ξ ( a ) = a . Second, we give the algebraic structure of ( x n - ( a + b w ) , ξ , η ) -skew constacyclic codes and their Hermitian dual codes over R = F q + w F q ( w 2 = w ) by decomposition theorem, where ξ is an automorphism and η a ξ -derivation of R , a + b w is a unit of R and ξ ( a + b w ) = a + b w . As an application, quantum codes from ( x n - ( a + b w ) , ξ , 0 ) -skew constacyclic codes over R are given by Hermitian construction and a Gray map between R and F q . Finally, we construct some good quantum codes by calculation.