MinT - Information on Result #980174

Information on Result #980174

Linear OOA(8⁸⁶, 185, F₈, 3, 28) (dual of [(185, 3), 469, 29]-NRT-code), using OOA 2-folding based on linear OOA(8⁸⁶, 370, F₈, 2, 28) (dual of [(370, 2), 654, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8⁸⁶, 371, F₈, 2, 28) (dual of [(371, 2), 656, 29]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹⁶, 17, F₈, 2, 14) (dual of [(17, 2), 18, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(8⁷⁰, 354, F₈, 2, 28) (dual of [(354, 2), 638, 29]-NRT-code), using
    - extracting embedded OOA [i] based on digital (42, 70, 354)-net over F₈, using
      - trace code for nets [i] based on digital (7, 35, 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.