Binary construction of pure additive quantum codes with distance five or six

This paper discusses binary quantum stabilizer codes with distance five or six constructed from binary self-orthogonal codes using Steane construction. First, nineteen special binary one-generator quasi-cyclic self-orthogonal (formula presented) codes with dual distance five or six for (formula presented) are built. Second, a feasible algorithm for searching subcodes of linear codes and an extension strategy for pairs of nested self-orthogonal codes are proposed, then thirty-eight code pairs are designed from obtained quasi-cyclic self-orthogonal codes. Third, thirty-two good binary quantum stabilizer codes are constructed from the code pairs obtained through Steane construction. Thirty of them are previously known codes. In particular, two codes (formula presented) and (formula presented) have improved codes (formula presented) and (formula presented) constructed by quaternary construction, and thus, they are record breaking ones.