MinT - Information on Result #875887

Information on Result #875887

Linear OOA(64⁷⁸, 101, F₆₄, 2, 58) (dual of [(101, 2), 124, 59]-NRT-code), using OOA 2-folding based on linear OA(64⁷⁸, 202, F₆₄, 58) (dual of [202, 124, 59]-code), using

discarding factors / shortening the dual code based on linear OA(64⁷⁸, 203, F₆₄, 58) (dual of [203, 125, 59]-code), using
- constructionÂ X applied to AG(F,117P) âŠ‚ AG(F,131P) [i] based on
  1. linear OA(64⁶⁵, 176, F₆₄, 58) (dual of [176, 111, 59]-code), using algebraic-geometric code AG(F,117P) [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(64⁵¹, 176, F₆₄, 44) (dual of [176, 125, 45]-code), using algebraic-geometric code AG(F,131P) [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.