MinT - Information on Result #2293210

Information on Result #2293210

OA(8¹⁶¹, 589, S₈, 56), using 1 times code embedding in larger space based on OA(8¹⁶⁰, 588, S₈, 56), using

trace code [i] based on OA(64⁸⁰, 294, S₆₄, 56), using
- discarding parts of the base [i] based on linear OA(128⁶⁸, 294, F₁₂₈, 56) (dual of [294, 226, 57]-code), using
  - constructionÂ X applied to AG(F,230P) âŠ‚ AG(F,234P) [i] based on
    1. linear OA(128⁶⁵, 287, F₁₂₈, 56) (dual of [287, 222, 57]-code), using algebraic-geometric code AG(F,230P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]
    2. linear OA(128⁶¹, 287, F₁₂₈, 52) (dual of [287, 226, 53]-code), using algebraic-geometric code AG(F,234P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
    3. linear OA(128³, 7, F₁₂₈, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,128) or 7-cap in PG(2,128)), using
      - discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
        Reedâ€“Solomon code RS(125,128) [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.