MinT - Information on Result #1235425

Information on Result #1235425

Linear OOA(2²³³, 2798244, F₂, 6, 12) (dual of [(2798244, 6), 16789231, 13]-NRT-code), using extracting embedded OOA based on digital (221, 233, 2798244)-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 (157, 169, 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, 138, 1398100)-net over F₂, using
      - net defined by OOA [i] based on linear OOA(2¹³⁸, 1398100, F₂, 12, 12) (dual of [(1398100, 12), 16777062, 13]-NRT-code), using
        OA 6-folding and stacking [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(2²³³, 2798243, F₂, 7, 12) (dual of [(2798243, 7), 19587468, 13]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2²³³, 2798243, F₂, 8, 12) (dual of [(2798243, 8), 22385711, 13]-NRT-code)	[i]		OOA Stacking with Additional Row