New quantum codes from two linear codes A CSS quantum code is succinctly represented as a pair of linear codes (C_1 ,C_2perp ) over finite fields mathbb F_pe with C_2perp subset C_1, where p is a prime and e is a positive integer. In this paper, we present two criteria of the C_2perp _ssubset C_1 , where C_2perp _s denotes the sGalois dual of C_2 and 0le s u003ce. Then, using the two criteria, we construct some new quantum codes and a class of new quantum maximumdistanceseparable (quantum MDS) codes. In addition, our obtained quantum MDS codes have parameters better than the ones available in the literature.

New stabilizer codes from the construction of dualcontaining matrixproduct codes Abstract   It is known from the CSS code construction that an          m  ,  2  k  xe2x88x92  m  ,  xe2x89xa5  d        q      stabilizer code can be obtained from a (Euclidean) dualcontaining        m  ,  k  ,  d      q      code. In  5 , Blackmore and Norton introduced an interesting code called matrixproduct code, which is very useful in constructing new quantum codes of large lengths. Recently, Galindo et al.  16  constructed several classes of stabilizer codes from the dualcontaining matrixproduct codes of (generalized) ReedMuller, hyperbolic and affine variety ones. In this paper, we first provide a more general approach to construct dualcontaining matrixproduct codes and then further study it in two cases. The first case generalizes the result by Galindo et al. and constructs dualcontaining matrixproduct codes more explicitly since the matrices involved are not restricted to be orthogonal. The second case presents a different way to construct dualcontaining matrixproduct codes in which some of the constituent codes are not required to be dualcontaining. Through the construction of dualcontaining matrixproduct codes of ReedMuller and affine variety ones, the CSS code construction and Steaneu0027s enlargement, we supply several classes of new stabilizer codes over the fields      F    5     ,      F    7      and      F    9      either having minimum distances larger than the ones achieved from the first case or the technique in  16 , or having lengths that are not studied in  16 .