MinT - Information on Result #1104854

Information on Result #1104854

Linear OOA(3²³⁰, 90, F₃, 5, 73) (dual of [(90, 5), 220, 74]-NRT-code), using OOA 2-folding based on linear OOA(3²³⁰, 180, F₃, 3, 73) (dual of [(180, 3), 310, 74]-NRT-code), using

trace code [i] based on linear OOA(9¹¹⁵, 90, F₉, 3, 73) (dual of [(90, 3), 155, 74]-NRT-code), using
- constructionÂ X applied to AG(3;F,157P) âŠ‚ AG(3;F,177P) [i] based on
  1. linear OOA(9⁹⁵, 77, F₉, 3, 73) (dual of [(77, 3), 136, 74]-NRT-code), using algebraic-geometric NRT-code AG(3;F,157P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]
  2. linear OOA(9⁷⁵, 77, F₉, 3, 53) (dual of [(77, 3), 156, 54]-NRT-code), using algebraic-geometric NRT-code AG(3;F,177P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9²⁰, 13, F₉, 3, 19) (dual of [(13, 3), 19, 20]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9²⁰, 16, F₉, 3, 19) (dual of [(16, 3), 28, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,28P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [i]

Mode: Constructive and linear.

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.