MinT - Information on Result #1143807

Information on Result #1143807

Linear OOA(2²²⁰, 1398179, F₂, 6, 17) (dual of [(1398179, 6), 8388854, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³², 78, F₂, 6, 8) (dual of [(78, 6), 436, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹¹, 47, F₂, 6, 4) (dual of [(47, 6), 271, 5]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(2¹¹, 47, F₂, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹¹, 47, F₂, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²¹, 39, F₂, 6, 8) (dual of [(39, 6), 213, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2¹⁸⁸, 1398101, F₂, 6, 17) (dual of [(1398101, 6), 8388418, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁸⁸, 2796202, F₂, 3, 17) (dual of [(2796202, 3), 8388418, 18]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁵, 2796201, F₂, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.