MinT - Information on Result #1821221

Information on Result #1821221

OA(128⁴⁴, 517, S₁₂₈, 25), using discarding parts of the base based on linear OA(256³⁸, 517, F₂₅₆, 25) (dual of [517, 479, 26]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256¹², 257, F₂₅₆, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using
  - extended Reedâ€“Solomon code RS_e(245,256) [i]
  - 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, using the rational function field F₂₅₆(x) [i]
  - algebraic-geometric code AG(F, Q+80P) with degQ = 4 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+48P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256²⁶, 260, F₂₅₆, 25) (dual of [260, 234, 26]-code), using
  - constructionÂ X applied to AG(F, Q+114P) âŠ‚ AG(F, Q+115P) [i] based on
    1. 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)
    2. linear OA(256²³, 257, F₂₅₆, 23) (dual of [257, 234, 24]-code or 257-arc in PG(22,256)), using algebraic-geometric code AG(F, Q+115P) 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(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.