Narrow Results

We give elementary recursive constructions of quaternary self-orthogonal codes with dual distance three for all n ≥ 5. Consequently, good linear quantum codes of minimum distance three for such length n are obtained. Almost all of these linear quantum codes are optimal or near optimal.

Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes. But for given restricted length n, good quantum BCH codes are very sparse. In this paper, by puncturing and pasting check matrices of Hermitian dual containing BCH codes over the quaternary field, we construct many linear quantum codes with good parameters, and some of them have parameters exceeding the finite Gilbert-Varshamov bound for stabilizer quantum codes.