MinT - Information on Result #859931

Information on Result #859931

Linear OOA(16¹¹⁵, 115, F₁₆, 2, 72) (dual of [(115, 2), 115, 73]-NRT-code), using OOA 2-folding based on linear OA(16¹¹⁵, 230, F₁₆, 72) (dual of [230, 115, 73]-code), using

discarding factors / shortening the dual code based on linear OA(16¹¹⁵, 231, F₁₆, 72) (dual of [231, 116, 73]-code), using
- constructionÂ X applied to AG(F,151P) âŠ‚ AG(F,155P) [i] based on
  1. linear OA(16¹¹², 224, F₁₆, 72) (dual of [224, 112, 73]-code), using algebraic-geometric code AG(F,151P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(16¹⁰⁸, 224, F₁₆, 68) (dual of [224, 116, 69]-code), using algebraic-geometric code AG(F,155P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OA(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
    - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
      - Reedâ€“Solomon code RS(13,16) [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.