MinT - Information on Result #1181244

Information on Result #1181244

Digital (216, 232, 1049598)-net over F₂, using net defined by OOA based on linear OOA(2²³², 1049598, F₂, 24, 16) (dual of [(1049598, 24), 25190120, 17]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2²³², 1049599, F₂, 8, 16) (dual of [(1049599, 8), 8396560, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁸, 1024, F₂, 8, 8) (dual of [(1024, 8), 8144, 9]-NRT-code), using
    - OA 4-folding and stacking [i] based on linear OA(2⁴⁸, 4096, F₂, 8) (dual of [4096, 4048, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁴⁹, 4097, F₂, 9) (dual of [4097, 4048, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OOA(2¹⁸⁴, 1048575, F₂, 8, 16) (dual of [(1048575, 8), 8388416, 17]-NRT-code), using
    - OOA 8-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.