MinT - Information on Result #2525646

Information on Result #2525646

OOA(8¹⁶³, 584, S₈, 2, 55), using 8¹ times duplication based on OOA(8¹⁶², 584, S₈, 2, 55), using

trace code [i] based on OOA(64⁸¹, 292, S₆₄, 2, 55), using
- discarding parts of the base [i] based on linear OOA(128⁶⁹, 292, F₁₂₈, 2, 55) (dual of [(292, 2), 515, 56]-NRT-code), using
  - constructionÂ X applied to AG(2;F,518P) âŠ‚ AG(2;F,524P) [i] based on
    1. linear OOA(128⁶⁴, 287, F₁₂₈, 2, 55) (dual of [(287, 2), 510, 56]-NRT-code), using algebraic-geometric NRT-code AG(2;F,518P) [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 OOA(128⁵⁸, 287, F₁₂₈, 2, 49) (dual of [(287, 2), 516, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,524P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
    3. linear OOA(128⁵, 5, F₁₂₈, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(128⁵, 128, F₁₂₈, 2, 5) (dual of [(128, 2), 251, 6]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;251,128) [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.