MinT - Information on Result #1181190

Information on Result #1181190

Digital (180, 196, 1048583)-net over F₂, using net defined by OOA based on linear OOA(2¹⁹⁶, 1048583, F₂, 24, 16) (dual of [(1048583, 24), 25165796, 17]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁹⁶, 1048584, F₂, 8, 16) (dual of [(1048584, 8), 8388476, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 9, F₂, 8, 8) (dual of [(9, 8), 60, 9]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹², 9, F₂, 7, 8) (dual of [(9, 7), 51, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 12, 9)-net over F₂, using
        linear code embedding found in a computer search [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.