MinT - Information on Result #1821484

Information on Result #1821484

OA(128⁷⁰, 517, S₁₂₈, 40), using discarding parts of the base based on linear OA(256⁶¹, 517, F₂₅₆, 40) (dual of [517, 456, 41]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256²⁰, 257, F₂₅₆, 20) (dual of [257, 237, 21]-code or 257-arc in PG(19,256)), using
  - extended Reedâ€“Solomon code RS_e(237,256) [i]
  - algebraic-geometric code AG(F,118P) 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]
  - algebraic-geometric code AG(F, Q+78P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  - algebraic-geometric code AG(F, Q+46P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256⁴¹, 260, F₂₅₆, 40) (dual of [260, 219, 41]-code), using
  - constructionÂ X applied to AG(F,108P) âŠ‚ AG(F,109P) [i] based on
    1. linear OA(256⁴⁰, 257, F₂₅₆, 40) (dual of [257, 217, 41]-code or 257-arc in PG(39,256)), using algebraic-geometric code AG(F,108P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    2. linear OA(256³⁸, 257, F₂₅₆, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) with 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.

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.