MinT - Information on Result #2287133

Information on Result #2287133

Linear OA(16¹¹⁷, 533, F₁₆, 54) (dual of [533, 416, 55]-code), using 1 times code embedding in larger space based on linear OA(16¹¹⁶, 532, F₁₆, 54) (dual of [532, 416, 55]-code), using

trace code [i] based on linear OA(256⁵⁸, 266, F₂₅₆, 54) (dual of [266, 208, 55]-code), using
- constructionÂ X applied to AG(F, Q+40P) âŠ‚ AG(F, Q+41P) [i] based on
  1. linear OA(256⁵⁴, 257, F₂₅₆, 54) (dual of [257, 203, 55]-code or 257-arc in PG(53,256)), using algebraic-geometric code AG(F,101P) 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(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 (see above)
  3. linear OA(256⁴, 9, F₂₅₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
      - Reedâ€“Solomon code RS(252,256) [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.