MinT - Information on Result #876112

Information on Result #876112

Linear OOA(64⁸⁸, 101, F₆₄, 2, 68) (dual of [(101, 2), 114, 69]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁸, 202, F₆₄, 68) (dual of [202, 114, 69]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁸, 203, F₆₄, 68) (dual of [203, 115, 69]-code), using
- constructionÂ X applied to AG(F,107P) âŠ‚ AG(F,121P) [i] based on
  1. linear OA(64⁷⁵, 176, F₆₄, 68) (dual of [176, 101, 69]-code), using algebraic-geometric code AG(F,107P) [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(64⁶¹, 176, F₆₄, 54) (dual of [176, 115, 55]-code), using algebraic-geometric code AG(F,121P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64¹³, 27, F₆₄, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,64)), using
    - discarding factors / shortening the dual code based on linear OA(64¹³, 64, F₆₄, 13) (dual of [64, 51, 14]-code or 64-arc in PG(12,64)), using
      - Reedâ€“Solomon code RS(51,64) [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.