MinT - Information on Result #981379

Information on Result #981379

Linear OOA(8¹³⁸, 209, F₈, 3, 44) (dual of [(209, 3), 489, 45]-NRT-code), using OOA 2-folding based on linear OOA(8¹³⁸, 418, F₈, 2, 44) (dual of [(418, 2), 698, 45]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8¹³⁸, 419, F₈, 2, 44) (dual of [(419, 2), 700, 45]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8³⁶, 65, F₈, 2, 22) (dual of [(65, 2), 94, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,107P) [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(8¹⁰², 354, F₈, 2, 44) (dual of [(354, 2), 606, 45]-NRT-code), using
    - extracting embedded OOA [i] based on digital (58, 102, 354)-net over F₈, using
      - trace code for nets [i] based on digital (7, 51, 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.