MinT - Information on Result #2287182

Information on Result #2287182

Linear OA(16¹²⁵, 533, F₁₆, 58) (dual of [533, 408, 59]-code), using 1 times code embedding in larger space based on linear OA(16¹²⁴, 532, F₁₆, 58) (dual of [532, 408, 59]-code), using

trace code [i] based on linear OA(256⁶², 266, F₂₅₆, 58) (dual of [266, 204, 59]-code), using
- constructionÂ X applied to AG(F, Q+39P) âŠ‚ AG(F, Q+40P) [i] based on
  1. linear OA(256⁵⁸, 257, F₂₅₆, 58) (dual of [257, 199, 59]-code or 257-arc in PG(57,256)), using algebraic-geometric code AG(F,99P) 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(256⁵³, 257, F₂₅₆, 53) (dual of [257, 204, 54]-code or 257-arc in PG(52,256)), using algebraic-geometric code AG(F, Q+100P) 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.