MinT - Information on Result #968571

Information on Result #968571

Linear OOA(4²⁵⁰, 141, F₄, 3, 89) (dual of [(141, 3), 173, 90]-NRT-code), using OOA 3-folding based on linear OA(4²⁵⁰, 423, F₄, 89) (dual of [423, 173, 90]-code), using

discarding factors / shortening the dual code based on linear OA(4²⁵⁰, 424, F₄, 89) (dual of [424, 174, 90]-code), using
- concatenation of two codes [i] based on
  1. linear OA(64⁴⁸, 106, F₆₄, 44) (dual of [106, 58, 45]-code), using
    - constructionÂ X applied to AG(F,58P) âŠ‚ AG(F,60P) [i] based on
      1. linear OA(64⁴⁷, 103, F₆₄, 44) (dual of [103, 56, 45]-code), using algebraic-geometric code AG(F,58P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]
      2. linear OA(64⁴⁵, 103, F₆₄, 42) (dual of [103, 58, 43]-code), using algebraic-geometric code AG(F,60P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (see above)
      3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.