MinT - Information on Result #2284891

Information on Result #2284891

Linear OA(9¹³⁷, 457, F₉, 53) (dual of [457, 320, 54]-code), using 1 times code embedding in larger space based on linear OA(9¹³⁶, 456, F₉, 53) (dual of [456, 320, 54]-code), using

trace code [i] based on linear OA(81⁶⁸, 228, F₈₁, 53) (dual of [228, 160, 54]-code), using
- constructionÂ X applied to AG(F,169P) âŠ‚ AG(F,172P) [i] based on
  1. linear OA(81⁶⁶, 223, F₈₁, 53) (dual of [223, 157, 54]-code), using algebraic-geometric code AG(F,169P) [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(81⁶³, 223, F₈₁, 50) (dual of [223, 160, 51]-code), using algebraic-geometric code AG(F,172P) [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.