MinT - Information on Result #875266

Information on Result #875266

Linear OOA(64⁵¹, 91, F₆₄, 2, 41) (dual of [(91, 2), 131, 42]-NRT-code), using OOA 2-folding based on linear OA(64⁵¹, 182, F₆₄, 41) (dual of [182, 131, 42]-code), using

discarding factors / shortening the dual code based on linear OA(64⁵¹, 183, F₆₄, 41) (dual of [183, 132, 42]-code), using
- constructionÂ X applied to AG(F,134P) âŠ‚ AG(F,138P) [i] based on
  1. linear OA(64⁴⁸, 176, F₆₄, 41) (dual of [176, 128, 42]-code), using algebraic-geometric code AG(F,134P) [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(64⁴⁴, 176, F₆₄, 37) (dual of [176, 132, 38]-code), using algebraic-geometric code AG(F,138P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64³, 7, F₆₄, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
    - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
      - Reedâ€“Solomon code RS(61,64) [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.