MinT - Information on Result #875921

Information on Result #875921

Linear OOA(64⁸⁶, 108, F₆₄, 2, 59) (dual of [(108, 2), 130, 60]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁶, 216, F₆₄, 59) (dual of [216, 130, 60]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁶, 217, F₆₄, 59) (dual of [217, 131, 60]-code), using
- constructionÂ X applied to AG(F,116P) âŠ‚ AG(F,137P) [i] based on
  1. linear OA(64⁶⁶, 176, F₆₄, 59) (dual of [176, 110, 60]-code), using algebraic-geometric code AG(F,116P) [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(64⁴⁵, 176, F₆₄, 38) (dual of [176, 131, 39]-code), using algebraic-geometric code AG(F,137P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64²⁰, 41, F₆₄, 20) (dual of [41, 21, 21]-code or 41-arc in PG(19,64)), using
    - discarding factors / shortening the dual code based on linear OA(64²⁰, 64, F₆₄, 20) (dual of [64, 44, 21]-code or 64-arc in PG(19,64)), using
      - Reedâ€“Solomon code RS(44,64) [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.