MinT - Information on Result #2287036

Information on Result #2287036

Linear OA(16¹⁰⁵, 529, F₁₆, 49) (dual of [529, 424, 50]-code), using 1 times code embedding in larger space based on linear OA(16¹⁰⁴, 528, F₁₆, 49) (dual of [528, 424, 50]-code), using

trace code [i] based on linear OA(256⁵², 264, F₂₅₆, 49) (dual of [264, 212, 50]-code), using
- constructionÂ X applied to AG(F, Q+102P) âŠ‚ AG(F, Q+104P) [i] based on
  1. linear OA(256⁴⁹, 257, F₂₅₆, 49) (dual of [257, 208, 50]-code or 257-arc in PG(48,256)), using algebraic-geometric code AG(F, Q+102P) 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(256⁴⁵, 257, F₂₅₆, 45) (dual of [257, 212, 46]-code or 257-arc in PG(44,256)), using algebraic-geometric code AG(F, Q+104P) 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(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.