New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

Abstract We study the algebraic structures of a generalized class of quasi-cyclic codes of index two, and prove that any quasi-cyclic codes of index two can be transformed into our proposed quasi-cyclic codes. We determine the generator forms of the proposed quasi-cyclic codes and their Hermitian dual codes. We establish the necessary and sufficient conditions for Hermitian self-orthogonality and dual-containing property to construct quantum stabilizer codes via the Hermitian construction method. As an application, 10 record-breaking quantum stabilizer codes are constructed.