MinT - Information on Result #2287166

Information on Result #2287166

Linear OA(16¹¹⁷, 521, F₁₆, 57) (dual of [521, 404, 58]-code), using 1 times code embedding in larger space based on linear OA(16¹¹⁶, 520, F₁₆, 57) (dual of [520, 404, 58]-code), using

trace code [i] based on linear OA(256⁵⁸, 260, F₂₅₆, 57) (dual of [260, 202, 58]-code), using
- constructionÂ X applied to AG(F, Q+98P) âŠ‚ AG(F, Q+99P) [i] based on
  1. linear OA(256⁵⁷, 257, F₂₅₆, 57) (dual of [257, 200, 58]-code or 257-arc in PG(56,256)), using algebraic-geometric code AG(F, Q+98P) 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(256⁵⁵, 257, F₂₅₆, 55) (dual of [257, 202, 56]-code or 257-arc in PG(54,256)), using algebraic-geometric code AG(F, Q+99P) 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(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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.