MinT - Information on Result #1191436

Information on Result #1191436

Digital (81, 92, 2796265)-net over F₈, using net defined by OOA based on linear OOA(8⁹², 2796265, F₈, 15, 11) (dual of [(2796265, 15), 41943883, 12]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁹², 5592531, F₈, 3, 11) (dual of [(5592531, 3), 16777501, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁹², 5592532, F₈, 3, 11) (dual of [(5592532, 3), 16777504, 12]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8¹⁰, 130, F₈, 3, 5) (dual of [(130, 3), 380, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (5, 10, 130)-net over F₈, using
        trace code for nets [i] based on digital (0, 5, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
    2. linear OOA(8⁸², 5592402, F₈, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
      - trace code [i] based on linear OOA(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.