MinT - Information on Result #1181204

Information on Result #1181204

Digital (187, 203, 1048604)-net over F₂, using net defined by OOA based on linear OOA(2²⁰³, 1048604, F₂, 24, 16) (dual of [(1048604, 24), 25166293, 17]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2²⁰³, 1048605, F₂, 8, 16) (dual of [(1048605, 8), 8388637, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁹, 30, F₂, 8, 8) (dual of [(30, 8), 221, 9]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁹, 30, F₂, 7, 8) (dual of [(30, 7), 191, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (11, 19, 30)-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.