MinT - Information on Result #1235487

Information on Result #1235487

Linear OOA(2¹⁷⁰, 1399122, F₂, 7, 13) (dual of [(1399122, 7), 9793684, 14]-NRT-code), using extracting embedded OOA based on digital (157, 170, 1399122)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (25, 31, 1022)-net over F₂, using
  - 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2³², 1022, F₂, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2³², 1023, F₂, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
2. digital (126, 139, 1398100)-net over F₂, using
  - net defined by OOA [i] based on linear OOA(2¹³⁹, 1398100, F₂, 13, 13) (dual of [(1398100, 13), 18175161, 14]-NRT-code), using
    - OOA 6-folding and stacking with additional row [i] based on linear OA(2¹³⁹, 8388601, F₂, 13) (dual of [8388601, 8388462, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁷², 1399122, F₂, 7, 13) (dual of [(1399122, 7), 9793682, 14]-NRT-code)	[i]		OOA Duplication