MinT - Information on Result #1235424

Information on Result #1235424

Linear OOA(2²³¹, 2797220, F₂, 6, 13) (dual of [(2797220, 6), 16783089, 14]-NRT-code), using extracting embedded OOA based on digital (218, 231, 2797220)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. 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]
2. digital (154, 167, 1398610)-net over F₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (22, 28, 510)-net over F₂, using
      - 1 times m-reduction [i] based on digital (22, 29, 510)-net over F₂, using
        net defined by OOA [i] based on linear OOA(2²⁹, 510, F₂, 7, 7) (dual of [(510, 7), 3541, 8]-NRT-code), using
        OOA stacking with additional row [i] based on linear OOA(2²⁹, 511, F₂, 3, 7) (dual of [(511, 3), 1504, 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		Method
1	Linear OOA(2²³³, 2797220, F₂, 6, 13) (dual of [(2797220, 6), 16783087, 14]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³¹, 2797219, F₂, 7, 13) (dual of [(2797219, 7), 19580302, 14]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(2²³¹, 2797219, F₂, 8, 13) (dual of [(2797219, 8), 22377521, 14]-NRT-code)	[i]	OOA Stacking with Additional Row