MinT - Information on Result #2284912

Information on Result #2284912

Linear OA(9¹⁴⁵, 749, F₉, 54) (dual of [749, 604, 55]-code), using 1 times code embedding in larger space based on linear OA(9¹⁴⁴, 748, F₉, 54) (dual of [748, 604, 55]-code), using

trace code [i] based on linear OA(81⁷², 374, F₈₁, 54) (dual of [374, 302, 55]-code), using
- constructionÂ X applied to AG(F,314P) âŠ‚ AG(F,317P) [i] based on
  1. linear OA(81⁷⁰, 369, F₈₁, 54) (dual of [369, 299, 55]-code), using algebraic-geometric code AG(F,314P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(81⁶⁷, 369, F₈₁, 51) (dual of [369, 302, 52]-code), using algebraic-geometric code AG(F,317P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OA(81², 5, F₈₁, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,81)), using
    - discarding factors / shortening the dual code based on linear OA(81², 81, F₈₁, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
      - Reedâ€“Solomon code RS(79,81) [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.