MinT - Information on Result #2709871

Information on Result #2709871

OOA(8¹⁶⁷, 582, S₈, 3, 56), using 8¹ times duplication based on OOA(8¹⁶⁶, 582, S₈, 3, 56), using

trace code [i] based on OOA(64⁸³, 291, S₆₄, 3, 56), using
- discarding parts of the base [i] based on linear OOA(128⁷¹, 291, F₁₂₈, 3, 56) (dual of [(291, 3), 802, 57]-NRT-code), using
  - constructionÂ X applied to AG(3;F,804P) âŠ‚ AG(3;F,811P) [i] based on
    1. linear OOA(128⁶⁵, 287, F₁₂₈, 3, 56) (dual of [(287, 3), 796, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,804P) [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, 3, 49) (dual of [(287, 3), 803, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,811P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
    3. linear OOA(128⁶, 4, F₁₂₈, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(128⁶, 128, F₁₂₈, 3, 6) (dual of [(128, 3), 378, 7]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;378,128) [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.