MinT - Information on Result #2287022

Information on Result #2287022

Linear OA(16¹¹⁷, 555, F₁₆, 48) (dual of [555, 438, 49]-code), using 3 times code embedding in larger space based on linear OA(16¹¹⁴, 552, F₁₆, 48) (dual of [552, 438, 49]-code), using

trace code [i] based on linear OA(256⁵⁷, 276, F₂₅₆, 48) (dual of [276, 219, 49]-code), using
- constructionÂ X applied to AG(F,104P) âŠ‚ AG(F,109P) [i] based on
  1. linear OA(256⁴⁸, 257, F₂₅₆, 48) (dual of [257, 209, 49]-code or 257-arc in PG(47,256)), using algebraic-geometric code AG(F,104P) 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(256⁹, 19, F₂₅₆, 9) (dual of [19, 10, 10]-code or 19-arc in PG(8,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁹, 256, F₂₅₆, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
      - Reedâ€“Solomon code RS(247,256) [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.