Quantum codes constructed from binary cyclic codes

In this paper, we use 2-cyclotomic cosets of modulo n and generator polynomials to describe binary cyclic codes of length N = 2(alpha)n with n odd. We discuss the conditions under which two cyclic codes C = [N, k, d] and C' = [N, k(1), d(1)] can be used to construct quantum codes by CSS construction or Steane's construction. Using the results of Chen, Promhouse and Tavares, and Castagnoli et al., we study the quantum codes that can be constructed from binary cyclic codes of length N = 2(alpha)n with n odd and n <= 99, and alpha <= 2. We find that except the quantum codes constructed by Steane, there are also some very interesting quantum codes constructed from repeated-root cyclic codes, and some of the quantum codes constructed by Steane can be improved.