MinT - Information on Result #876144

Information on Result #876144

Linear OOA(64⁸⁹, 100, F₆₄, 2, 70) (dual of [(100, 2), 111, 71]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁹, 200, F₆₄, 70) (dual of [200, 111, 71]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁹, 201, F₆₄, 70) (dual of [201, 112, 71]-code), using
- constructionÂ X applied to AG(F,105P) âŠ‚ AG(F,118P) [i] based on
  1. linear OA(64⁷⁷, 176, F₆₄, 70) (dual of [176, 99, 71]-code), using algebraic-geometric code AG(F,105P) [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(64⁶⁴, 176, F₆₄, 57) (dual of [176, 112, 58]-code), using algebraic-geometric code AG(F,118P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64¹², 25, F₆₄, 12) (dual of [25, 13, 13]-code or 25-arc in PG(11,64)), using
    - discarding factors / shortening the dual code based on linear OA(64¹², 64, F₆₄, 12) (dual of [64, 52, 13]-code or 64-arc in PG(11,64)), using
      - Reedâ€“Solomon code RS(52,64) [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.