MinT - Information on Result #1821296

Information on Result #1821296

OA(128⁵², 522, S₁₂₈, 28), using discarding parts of the base based on linear OA(256⁴⁵, 522, F₂₅₆, 28) (dual of [522, 477, 29]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256¹⁵, 260, F₂₅₆, 14) (dual of [260, 245, 15]-code), using
  - constructionÂ X applied to AG(F,121P) âŠ‚ AG(F,122P) [i] based on
    1. linear OA(256¹⁴, 257, F₂₅₆, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using algebraic-geometric code AG(F,121P) 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(256¹², 257, F₂₅₆, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using algebraic-geometric code AG(F,122P) 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]
2. linear OA(256³⁰, 262, F₂₅₆, 28) (dual of [262, 232, 29]-code), using
  - constructionÂ X applied to AG(F,76P) âŠ‚ AG(F,77P) [i] based on
    1. linear OA(256²⁸, 257, F₂₅₆, 28) (dual of [257, 229, 29]-code or 257-arc in PG(27,256)), using algebraic-geometric code AG(F,114P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    2. linear OA(256²⁵, 257, F₂₅₆, 25) (dual of [257, 232, 26]-code or 257-arc in PG(24,256)), using algebraic-geometric code AG(F, Q+114P) 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.

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.