MinT - Information on Result #876170

Information on Result #876170

Linear OOA(64⁸⁸, 97, F₆₄, 2, 72) (dual of [(97, 2), 106, 73]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁸, 194, F₆₄, 72) (dual of [194, 106, 73]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁸, 195, F₆₄, 72) (dual of [195, 107, 73]-code), using
- constructionÂ X applied to AG(F,103P) âŠ‚ AG(F,113P) [i] based on
  1. linear OA(64⁷⁹, 176, F₆₄, 72) (dual of [176, 97, 73]-code), using algebraic-geometric code AG(F,103P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(64⁶⁹, 176, F₆₄, 62) (dual of [176, 107, 63]-code), using algebraic-geometric code AG(F,113P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64⁹, 19, F₆₄, 9) (dual of [19, 10, 10]-code or 19-arc in PG(8,64)), using
    - discarding factors / shortening the dual code based on linear OA(64⁹, 64, F₆₄, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
      - Reedâ€“Solomon code RS(55,64) [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.