MinT - Information on Result #980827

Information on Result #980827

Linear OOA(8¹¹³, 199, F₈, 3, 36) (dual of [(199, 3), 484, 37]-NRT-code), using OOA 2-folding based on linear OOA(8¹¹³, 398, F₈, 2, 36) (dual of [(398, 2), 683, 37]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8¹¹³, 399, F₈, 2, 36) (dual of [(399, 2), 685, 37]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8²⁷, 45, F₈, 2, 18) (dual of [(45, 2), 63, 19]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,71P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(8⁸⁶, 354, F₈, 2, 36) (dual of [(354, 2), 622, 37]-NRT-code), using
    - extracting embedded OOA [i] based on digital (50, 86, 354)-net over F₈, using
      - trace code for nets [i] based on digital (7, 43, 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.