MinT - Information on Result #2286817

Information on Result #2286817

Linear OA(16¹⁰¹, 561, F₁₆, 39) (dual of [561, 460, 40]-code), using 1 times code embedding in larger space based on linear OA(16¹⁰⁰, 560, F₁₆, 39) (dual of [560, 460, 40]-code), using

trace code [i] based on linear OA(256⁵⁰, 280, F₂₅₆, 39) (dual of [280, 230, 40]-code), using
- constructionÂ X applied to AG(F, Q+107P) âŠ‚ AG(F, Q+113P) [i] based on
  1. linear OA(256³⁹, 257, F₂₅₆, 39) (dual of [257, 218, 40]-code or 257-arc in PG(38,256)), using algebraic-geometric code AG(F, Q+107P) with degQ = 3 and 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(256²⁷, 257, F₂₅₆, 27) (dual of [257, 230, 28]-code or 257-arc in PG(26,256)), using algebraic-geometric code AG(F, Q+113P) 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(256¹¹, 23, F₂₅₆, 11) (dual of [23, 12, 12]-code or 23-arc in PG(10,256)), using
    - discarding factors / shortening the dual code based on linear OA(256¹¹, 256, F₂₅₆, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
      - Reedâ€“Solomon code RS(245,256) [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.