New quantum codes from matrix-product codes over small fields

In this paper, we provide methods for constructing Hermitian dual-containing (HDC) matrix-product codes over F q 2 from some non-singular matrices and a special sequence of HDC codes and determine parameters of obtained matrix-product codes when the input matrix and sequence of HDC codes satisfy some conditions. Then, using some nested HDC BCH codes with lengths n = q 4 - 1 a ( a = 1 or a = q ± 1 ) , we construct some HDC matrix-product codes with lengths N = 2 n or 3 n and derive nonbinary quantum codes with length N from these matrix-product codes via Hermitian construction. Four classes of quantum codes over F q ( 3 ≤ q ≤ 5 ) are presented, whose parameters are better than those in the literature. Besides, some of our new quantum codes can exceed the quantum Gilbert-Varshamov (GV) bound.