Ternary self-orthogonal codes of dual distance three and ternary quantum codes of distance three

Abstract

Ternary self-orthogonal codes with dual distance three and ternary quantum codes of distance three constructed from ternary self-orthogonal codes are discussed in this paper. Firstly, for given code length n ≥ 8, a ternary [n, k]3 self-orthogonal code with minimal dimension k and dual distance three is constructed. Secondly, for each n ≥ 8, two nested ternary self-orthogonal codes with dual distance two and three are constructed, and consequently ternary quantum code of length n and distance three is constructed via Steane construction. Almost all of these quantum codes constructed via Steane construction are optimal or near optimal, and some of these quantum codes are better than those known before.