MinT - Information on Result #2287069

Information on Result #2287069

Linear OA(16¹²⁵, 563, F₁₆, 50) (dual of [563, 438, 51]-code), using 3 times code embedding in larger space based on linear OA(16¹²², 560, F₁₆, 50) (dual of [560, 438, 51]-code), using

trace code [i] based on linear OA(256⁶¹, 280, F₂₅₆, 50) (dual of [280, 219, 51]-code), using
- constructionÂ X applied to AG(F,103P) âŠ‚ AG(F,109P) [i] based on
  1. linear OA(256⁵⁰, 257, F₂₅₆, 50) (dual of [257, 207, 51]-code or 257-arc in PG(49,256)), using algebraic-geometric code AG(F,103P) 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(256³⁸, 257, F₂₅₆, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) with 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.