MinT - Information on Result #941076

Information on Result #941076

Linear OOA(8¹²³, 421, F₈, 2, 37) (dual of [(421, 2), 719, 38]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³⁵, 67, F₈, 2, 18) (dual of [(67, 2), 99, 19]-NRT-code), using
- constructionÂ X applied to AG(2;F,109P) âŠ‚ AG(2;F,113P) [i] based on
  1. linear OOA(8³², 64, F₈, 2, 18) (dual of [(64, 2), 96, 19]-NRT-code), using algebraic-geometric NRT-code AG(2;F,109P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]
  2. linear OOA(8²⁸, 64, F₈, 2, 14) (dual of [(64, 2), 100, 15]-NRT-code), using algebraic-geometric NRT-code AG(2;F,113P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8³, 3, F₈, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8³, 8, F₈, 2, 3) (dual of [(8, 2), 13, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;13,8) [i]
linear OOA(8⁸⁸, 354, F₈, 2, 37) (dual of [(354, 2), 620, 38]-NRT-code), using
- extracting embedded OOA [i] based on digital (51, 88, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 44, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, 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.