MinT - Information on Result #1235022

Information on Result #1235022

Linear OOA(2²¹², 4194309, F₂, 4, 13) (dual of [(4194309, 4), 16777024, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097150, F₂, 4, 6) (dual of [(2097150, 4), 8388536, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (58, 64, 2097150)-net over F₂, using
  - 1 times m-reduction [i] based on digital (58, 65, 2097150)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
linear OOA(2¹⁴⁸, 2097159, F₂, 4, 13) (dual of [(2097159, 4), 8388488, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 9, F₂, 4, 6) (dual of [(9, 4), 27, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 9, 9)-net over F₂, using
      - a shift-net [i]
  2. linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.