The construction of quantum quasi-cyclic codes based on the Hermitian inner product

In order to construct quantum stabilizer codes with high-error-correcting performance, in this paper, we propose a wide class of quasi-cyclic codes, providing the generator forms and code parameters of such codes and their Hermitian dual codes. By giving the 条件 for the Hermitian self-orthogonality of such quasi-cyclic codes, we obtain a new class of quantum quasi-cyclic codes according to the Hermitian construction. Among this class of quantum quasi-cyclic codes, we find 12 record-breaking binary quantum stabilizer codes. Their minimum distances are higher than those of the corresponding codes in existing quantum code tables. These results demonstrate that our method provides effective support for the construction of quantum stabilizer codes with high-error-correcting performance.