MinT - Information on Result #2284809

Information on Result #2284809

Linear OA(9¹²⁹, 457, F₉, 49) (dual of [457, 328, 50]-code), using 1 times code embedding in larger space based on linear OA(9¹²⁸, 456, F₉, 49) (dual of [456, 328, 50]-code), using

trace code [i] based on linear OA(81⁶⁴, 228, F₈₁, 49) (dual of [228, 164, 50]-code), using
- constructionÂ X applied to AG(F,173P) âŠ‚ AG(F,176P) [i] based on
  1. linear OA(81⁶², 223, F₈₁, 49) (dual of [223, 161, 50]-code), using algebraic-geometric code AG(F,173P) [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]
  2. linear OA(81⁵⁹, 223, F₈₁, 46) (dual of [223, 164, 47]-code), using algebraic-geometric code AG(F,176P) [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224 (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.