MinT - Information on Result #858713

Information on Result #858713

Linear OOA(16¹²⁰, 284, F₁₆, 2, 47) (dual of [(284, 2), 448, 48]-NRT-code), using OOA 2-folding based on linear OA(16¹²⁰, 568, F₁₆, 47) (dual of [568, 448, 48]-code), using

trace code [i] based on linear OA(256⁶⁰, 284, F₂₅₆, 47) (dual of [284, 224, 48]-code), using
- constructionÂ X applied to AG(F, Q+103P) âŠ‚ AG(F, Q+110P) [i] based on
  1. linear OA(256⁴⁷, 257, F₂₅₆, 47) (dual of [257, 210, 48]-code or 257-arc in PG(46,256)), using algebraic-geometric code AG(F, Q+103P) 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(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(256¹³, 27, F₂₅₆, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,256)), using
    - discarding factors / shortening the dual code based on linear OA(256¹³, 256, F₂₅₆, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), using
      - Reedâ€“Solomon code RS(243,256) [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.