MinT - Information on Result #858937

Information on Result #858937

Linear OOA(16¹³⁰, 286, F₁₆, 2, 51) (dual of [(286, 2), 442, 52]-NRT-code), using OOA 2-folding based on linear OA(16¹³⁰, 572, F₁₆, 51) (dual of [572, 442, 52]-code), using

trace code [i] based on linear OA(256⁶⁵, 286, F₂₅₆, 51) (dual of [286, 221, 52]-code), using
- constructionÂ X applied to AG(F, Q+67P) âŠ‚ AG(F, Q+72P) [i] based on
  1. linear OA(256⁵¹, 257, F₂₅₆, 51) (dual of [257, 206, 52]-code or 257-arc in PG(50,256)), using algebraic-geometric code AG(F, Q+101P) 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(256³⁶, 257, F₂₅₆, 36) (dual of [257, 221, 37]-code or 257-arc in PG(35,256)), using algebraic-geometric code AG(F,110P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256¹⁴, 29, F₂₅₆, 14) (dual of [29, 15, 15]-code or 29-arc in PG(13,256)), using
    - discarding factors / shortening the dual code based on linear OA(256¹⁴, 256, F₂₅₆, 14) (dual of [256, 242, 15]-code or 256-arc in PG(13,256)), using
      - Reedâ€“Solomon code RS(242,256) [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.