Construction of Quantum Codes From Matrix-Product Codes

Recently, the construction of matrix-product codes with certain self-orthogonality is an effective way to obtain good quantum codes. One of the most frequently used means in this process is to construct quasi-unitary matrices as the defining matrices of matrix-product codes. Further, if the defining matrix is NSC, then the corresponding matrix-product code has maximal minimum distance. Inspired by these idea, we propose a constructive method about NSC quasi-unitary matrices over F
_q
2 with q being a prime power, and construct k × k NSC quasi-unitary matrices for any k <; q by certain properties of the polynomial ring F
_q
[x
₁
, . . . , x
_k
], extending or improving the known results. Through such defining matrices, we obtain new classes of quantum codes from matrix-product codes, many of which show better parameters than previously known.