MinT - Information on Result #2286507

Information on Result #2286507

Linear OA(16⁵⁹, 529, F₁₆, 26) (dual of [529, 470, 27]-code), using 1 times code embedding in larger space based on linear OA(16⁵⁸, 528, F₁₆, 26) (dual of [528, 470, 27]-code), using

trace code [i] based on linear OA(256²⁹, 264, F₂₅₆, 26) (dual of [264, 235, 27]-code), using
- constructionÂ X applied to AG(F,115P) âŠ‚ AG(F,117P) [i] based on
  1. 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, using the rational function field F₂₅₆(x) [i]
  2. linear OA(256²², 257, F₂₅₆, 22) (dual of [257, 235, 23]-code or 257-arc in PG(21,256)), using algebraic-geometric code AG(F,117P) 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.