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

Abstract

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 $$[pk,k]$$[pk,k] codes with dual distance five or six for $$12 \le k \le 16$$12≤k≤16 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 $$[[52,31,6]]$$[[52,31,6]] and $$[[56,34,6]]$$[[56,34,6]] have improved codes $$[[52,31,5]]$$[[52,31,5]] and $$[[56,34,5]]$$[[56,34,5]] constructed by quaternary construction, and thus, they are record breaking ones.