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 $$[pk,k]$$ [ p k , 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.
Quantum Information Processing – Springer Journals
Published: Oct 15, 2014
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