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

Abstract

It is known from the CSS code construction that an [[m,2k−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 F5, F7 and F9 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].