MinT - Information on Result #1822170

Information on Result #1822170

OA(128⁷³, 548, S₁₂₈, 40), using (u,Â u+v)-construction based on

OA(128²⁴, 260, S₁₂₈, 20), using
- discarding parts of the base [i] based on linear OA(256²¹, 260, F₂₅₆, 20) (dual of [260, 239, 21]-code), using
  - constructionÂ X applied to AG(F,118P) âŠ‚ AG(F,119P) [i] based on
    1. linear OA(256²⁰, 257, F₂₅₆, 20) (dual of [257, 237, 21]-code or 257-arc in PG(19,256)), using 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]
    2. linear OA(256¹⁸, 257, F₂₅₆, 18) (dual of [257, 239, 19]-code or 257-arc in PG(17,256)), using algebraic-geometric code AG(F,119P) 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]
linear OA(128⁴⁹, 288, F₁₂₈, 40) (dual of [288, 239, 41]-code), using
- extended algebraic-geometric code AG_e(F,247P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
  - a function field by SÃ©mirat [i]

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