MinT - Information on Result #1180278

Information on Result #1180278

Digital (144, 156, 1398163)-net over F₂, using net defined by OOA based on linear OOA(2¹⁵⁶, 1398163, F₂, 18, 12) (dual of [(1398163, 18), 25166778, 13]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁵⁶, 1398164, F₂, 6, 12) (dual of [(1398164, 6), 8388828, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁸, 64, F₂, 6, 6) (dual of [(64, 6), 366, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁸, 64, F₂, 5, 6) (dual of [(64, 5), 302, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 18, 64)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 1398100, F₂, 6, 12) (dual of [(1398100, 6), 8388462, 13]-NRT-code), using
    - OOA 6-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.