MinT - Information on Result #875639

Information on Result #875639

Linear OOA(64⁷⁴, 105, F₆₄, 2, 50) (dual of [(105, 2), 136, 51]-NRT-code), using OOA 2-folding based on linear OA(64⁷⁴, 210, F₆₄, 50) (dual of [210, 136, 51]-code), using

discarding factors / shortening the dual code based on linear OA(64⁷⁴, 211, F₆₄, 50) (dual of [211, 137, 51]-code), using
- constructionÂ X applied to AG(F,125P) âŠ‚ AG(F,143P) [i] based on
  1. linear OA(64⁵⁷, 176, F₆₄, 50) (dual of [176, 119, 51]-code), using algebraic-geometric code AG(F,125P) [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(64³⁹, 176, F₆₄, 32) (dual of [176, 137, 33]-code), using algebraic-geometric code AG(F,143P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64¹⁷, 35, F₆₄, 17) (dual of [35, 18, 18]-code or 35-arc in PG(16,64)), using
    - discarding factors / shortening the dual code based on linear OA(64¹⁷, 64, F₆₄, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), using
      - Reedâ€“Solomon code RS(47,64) [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.