MinT - Information on Result #827899

Information on Result #827899

Linear OOA(4¹⁹³, 281, F₄, 2, 52) (dual of [(281, 2), 369, 53]-NRT-code), using OOA 2-folding based on linear OA(4¹⁹³, 562, F₄, 52) (dual of [562, 369, 53]-code), using

1 times code embedding in larger space [i] based on linear OA(4¹⁹², 561, F₄, 52) (dual of [561, 369, 53]-code), using
- trace code [i] based on linear OA(64⁶⁴, 187, F₆₄, 52) (dual of [187, 123, 53]-code), using
  - constructionÂ X applied to AG(F,123P) âŠ‚ AG(F,129P) [i] based on
    1. linear OA(64⁵⁹, 176, F₆₄, 52) (dual of [176, 117, 53]-code), using algebraic-geometric code AG(F,123P) [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(64⁵³, 176, F₆₄, 46) (dual of [176, 123, 47]-code), using algebraic-geometric code AG(F,129P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
    3. linear OA(64⁵, 11, F₆₄, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,64)), using
      - discarding factors / shortening the dual code based on linear OA(64⁵, 64, F₆₄, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
        Reedâ€“Solomon code RS(59,64) [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.