MinT - Information on Result #1203496

Information on Result #1203496

Digital (46, 59, 1398239)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁵⁹, 1398239, F₁₂₈, 15, 13) (dual of [(1398239, 15), 20973526, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(128⁵⁹, 2796479, F₁₂₈, 3, 13) (dual of [(2796479, 3), 8389378, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁵⁹, 2796480, F₁₂₈, 3, 13) (dual of [(2796480, 3), 8389381, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(128¹⁰, 279, F₁₂₈, 3, 6) (dual of [(279, 3), 827, 7]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(128³, 129, F₁₂₈, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;384,128) [i]
        linear OOA(128⁷, 150, F₁₂₈, 3, 6) (dual of [(150, 3), 443, 7]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,443P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
    2. linear OOA(128⁴⁹, 2796201, F₁₂₈, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(128⁴⁹, large, F₁₂₈, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.