MinT - Information on Result #1179862

Information on Result #1179862

Digital (113, 123, 1677729)-net over F₂, using net defined by OOA based on linear OOA(2¹²³, 1677729, F₂, 15, 10) (dual of [(1677729, 15), 25165812, 11]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹²³, 1677730, F₂, 5, 10) (dual of [(1677730, 5), 8388527, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁸, 10, F₂, 5, 5) (dual of [(10, 5), 42, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁸, 10, F₂, 4, 5) (dual of [(10, 4), 32, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (3, 8, 10)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹¹⁵, 1677720, F₂, 5, 10) (dual of [(1677720, 5), 8388485, 11]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹¹⁵, 8388600, F₂, 10) (dual of [8388600, 8388485, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹¹⁵, large, F₂, 10) (dual of [large, large−115, 11]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.