MinT - Information on Result #2286885

Information on Result #2286885

Linear OA(16¹⁰¹, 549, F₁₆, 42) (dual of [549, 448, 43]-code), using 1 times code embedding in larger space based on linear OA(16¹⁰⁰, 548, F₁₆, 42) (dual of [548, 448, 43]-code), using

trace code [i] based on linear OA(256⁵⁰, 274, F₂₅₆, 42) (dual of [274, 224, 43]-code), using
- constructionÂ X applied to AG(F, Q+70P) âŠ‚ AG(F, Q+73P) [i] based on
  1. linear OA(256⁴², 257, F₂₅₆, 42) (dual of [257, 215, 43]-code or 257-arc in PG(41,256)), using algebraic-geometric code AG(F,107P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
  2. linear OA(256³³, 257, F₂₅₆, 33) (dual of [257, 224, 34]-code or 257-arc in PG(32,256)), using algebraic-geometric code AG(F, Q+110P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256⁸, 17, F₂₅₆, 8) (dual of [17, 9, 9]-code or 17-arc in PG(7,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁸, 256, F₂₅₆, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
      - Reedâ€“Solomon code RS(248,256) [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.