Hermitian dual-containing constacyclic codes over

In this paper, we study Hermitian dual-containing constacyclic codes over the finite ring R r = F q 2 + v 1 F q 2 + ⋯ + v r F q 2 , where q is a prime power and v i 2 = v i , v i v j = v j v i = 0 for 1 ≤ i , j ≤ r , i ≠ j . A necessary and sufficient condition is provided to determine whether a constacyclic code C over R r is Hermitian dual-containing. Moreover, we propose a generalized Gray map Φ M to preserve the property of Hermitian dual-containing. Compared with some existing Gray maps, Φ M increases the possibility of making the minimum distance of Φ M ( C ) larger. As an application, some new quantum codes over F q are constructed from constacyclic codes over R r .