MinT - Information on Result #2287056

Information on Result #2287056

Linear OA(16¹⁰⁵, 525, F₁₆, 50) (dual of [525, 420, 51]-code), using 1 times code embedding in larger space based on linear OA(16¹⁰⁴, 524, F₁₆, 50) (dual of [524, 420, 51]-code), using

trace code [i] based on linear OA(256⁵², 262, F₂₅₆, 50) (dual of [262, 210, 51]-code), using
- constructionÂ X applied to AG(F, Q+68P) âŠ‚ AG(F, Q+69P) [i] based on
  1. linear OA(256⁵⁰, 257, F₂₅₆, 50) (dual of [257, 207, 51]-code or 257-arc in PG(49,256)), using algebraic-geometric code AG(F,103P) 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(256⁴⁷, 257, F₂₅₆, 47) (dual of [257, 210, 48]-code or 257-arc in PG(46,256)), using algebraic-geometric code AG(F, Q+103P) 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(256², 5, F₂₅₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
    - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
      - Reedâ€“Solomon code RS(254,256) [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.