MinT - Information on Result #857522

Information on Result #857522

Linear OOA(16⁶⁶, 264, F₁₆, 2, 30) (dual of [(264, 2), 462, 31]-NRT-code), using OOA 2-folding based on linear OA(16⁶⁶, 528, F₁₆, 30) (dual of [528, 462, 31]-code), using

trace code [i] based on linear OA(256³³, 264, F₂₅₆, 30) (dual of [264, 231, 31]-code), using
- constructionÂ X applied to AG(F,113P) âŠ‚ AG(F,115P) [i] based on
  1. linear OA(256³⁰, 257, F₂₅₆, 30) (dual of [257, 227, 31]-code or 257-arc in PG(29,256)), using algebraic-geometric code AG(F,113P) 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(256²⁶, 257, F₂₅₆, 26) (dual of [257, 231, 27]-code or 257-arc in PG(25,256)), using algebraic-geometric code AG(F,115P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256³, 7, F₂₅₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,256) or 7-cap in PG(2,256)), using
    - discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
      - Reedâ€“Solomon code RS(253,256) [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.