MinT - Information on Result #858823

Information on Result #858823

Linear OOA(16¹¹², 272, F₁₆, 2, 49) (dual of [(272, 2), 432, 50]-NRT-code), using OOA 2-folding based on linear OA(16¹¹², 544, F₁₆, 49) (dual of [544, 432, 50]-code), using

trace code [i] based on linear OA(256⁵⁶, 272, F₂₅₆, 49) (dual of [272, 216, 50]-code), using
- constructionÂ X applied to AG(F, Q+102P) âŠ‚ AG(F, Q+106P) [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(256⁴¹, 257, F₂₅₆, 41) (dual of [257, 216, 42]-code or 257-arc in PG(40,256)), using algebraic-geometric code AG(F, Q+106P) 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(256⁷, 15, F₂₅₆, 7) (dual of [15, 8, 8]-code or 15-arc in PG(6,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁷, 256, F₂₅₆, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
      - Reedâ€“Solomon code RS(249,256) [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.