MinT - Information on Result #857284

Information on Result #857284

Linear OOA(16⁵⁸, 262, F₁₆, 2, 27) (dual of [(262, 2), 466, 28]-NRT-code), using OOA 2-folding based on linear OA(16⁵⁸, 524, F₁₆, 27) (dual of [524, 466, 28]-code), using

trace code [i] based on linear OA(256²⁹, 262, F₂₅₆, 27) (dual of [262, 233, 28]-code), using
- constructionÂ X applied to AG(F, Q+75P) âŠ‚ AG(F, Q+76P) [i] based on
  1. linear OA(256²⁷, 257, F₂₅₆, 27) (dual of [257, 230, 28]-code or 257-arc in PG(26,256)), using algebraic-geometric code AG(F, Q+113P) 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(256²⁴, 257, F₂₅₆, 24) (dual of [257, 233, 25]-code or 257-arc in PG(23,256)), using algebraic-geometric code AG(F,116P) with 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.