New stabilizer codes from the construction of dual-containing matrix-product codes

Abstract It is known from the CSS code construction that an [ [ m , 2 k − m , ≥ d ] ] q stabilizer code can be obtained from a (Euclidean) dual-containing [ m , k , d ] q code. In [5] , Blackmore and Norton introduced an interesting code called matrix-product 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 dual-containing matrix-product codes of (generalized) Reed-Muller, hyperbolic and affine variety ones. In this paper, we first provide a more general approach to construct dual-containing matrix-product codes and then further study it in two cases. The first case generalizes the result by Galindo et al. and constructs dual-containing matrix-product codes more explicitly since the matrices involved are not restricted to be orthogonal. The second case presents a different way to construct dual-containing matrix-product codes in which some of the constituent codes are not required to be dual-containing. Through the construction of dual-containing matrix-product codes of Reed-Muller and affine variety ones, the CSS code construction and Steane's 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] .