MinT - Information on Result #1822186

Information on Result #1822186

OA(128⁷⁰, 548, S₁₂₈, 38), using (u,Â u+v)-construction based on

OA(128²³, 260, S₁₂₈, 19), using
- discarding parts of the base [i] based on linear OA(256²⁰, 260, F₂₅₆, 19) (dual of [260, 240, 20]-code), using
  - constructionÂ X applied to AG(F, Q+117P) âŠ‚ AG(F, Q+118P) [i] based on
    1. linear OA(256¹⁹, 257, F₂₅₆, 19) (dual of [257, 238, 20]-code or 257-arc in PG(18,256)), using algebraic-geometric code AG(F, Q+117P) 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(256¹⁷, 257, F₂₅₆, 17) (dual of [257, 240, 18]-code or 257-arc in PG(16,256)), using algebraic-geometric code AG(F, Q+118P) 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]
linear OA(128⁴⁷, 288, F₁₂₈, 38) (dual of [288, 241, 39]-code), using
- extended algebraic-geometric code AG_e(F,249P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
  - a function field by SÃ©mirat [i]

None.

None.