Binary Generalized Quasi-Cyclic Self-orthogonal Codes and Binary Construction of Pure Quantum Codes

In this paper, a special subclass of binary generalized quasi-cyclic self-orthogonal codes and quantum codes constructed by Steane construction are discussed. Firstly, eight 16-dimensional even length generalized quasi-cyclic self-orthogonal codes with dual distance five are built based on circulant or partial circulant matrices. Secondly, pairs of nested self-orthogonal codes with dual distance five and three are designed by applying an algorithm for searching subcodes of a given code. Thirdly, revised pairs of codes with dual distance six and four are constructed by extending previous pairs of codes, and then eight quantum codes with distance six are obtained by Steane construction. These eight quantum codes are new binary construction by Steane construction and are best known ones. Index Terms - Quantum code, Steane construction, self- orthogonal code, generalized quasi-cyclic code, pair of nested self- orthogonal codes.