MinT - Information on Result #1181408

Information on Result #1181408

Digital (179, 196, 1048581)-net over F₂, using net defined by OOA based on linear OOA(2¹⁹⁶, 1048581, F₂, 24, 17) (dual of [(1048581, 24), 25165748, 18]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁹⁶, 1048582, F₂, 8, 17) (dual of [(1048582, 8), 8388460, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹¹, 7, F₂, 8, 8) (dual of [(7, 8), 45, 9]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹¹, 7, F₂, 7, 8) (dual of [(7, 7), 38, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(7;F,40P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁸⁵, 1048575, F₂, 8, 17) (dual of [(1048575, 8), 8388415, 18]-NRT-code), using
    - OOA 8-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.