MinT - Information on Result #1094452

Information on Result #1094452

Linear OOA(2⁹⁹, 2097157, F₂, 5, 9) (dual of [(2097157, 5), 10485686, 10]-NRT-code), using OOA stacking with additional row based on linear OOA(2⁹⁹, 2097158, F₂, 4, 9) (dual of [(2097158, 4), 8388533, 10]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶, 8, F₂, 4, 4) (dual of [(8, 4), 26, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁶, 8, F₂, 3, 4) (dual of [(8, 3), 18, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 6, 8)-net over F₂, using
      - hand-crafted matrix by Schmid and Wolf [i]
2. linear OOA(2⁹³, 2097150, F₂, 4, 9) (dual of [(2097150, 4), 8388507, 10]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2⁹³, 8388600, F₂, 9) (dual of [8388600, 8388507, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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.

Other Results with Identical Parameters

None.

Depending Results

None.