MinT - Information on Result #1009461

Information on Result #1009461

Linear OOA(2²⁵³, 2839891, F₂, 3, 17) (dual of [(2839891, 3), 8519420, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁸, 43690, F₂, 3, 8) (dual of [(43690, 3), 131002, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁶⁸, 131070, F₂, 8) (dual of [131070, 131002, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁶⁸, 131072, F₂, 8) (dual of [131072, 131004, 9]-code), using
    - 1 times truncation [i] based on linear OA(2⁶⁹, 131073, F₂, 9) (dual of [131073, 131004, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵³, 2839891, F₂, 4, 17) (dual of [(2839891, 4), 11359311, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵³, 2839891, F₂, 5, 17) (dual of [(2839891, 5), 14199202, 18]-NRT-code)	[i]
3	Linear OOA(2²⁵³, 2839891, F₂, 6, 17) (dual of [(2839891, 6), 17039093, 18]-NRT-code)	[i]
4	Linear OOA(2²⁵³, 2839891, F₂, 7, 17) (dual of [(2839891, 7), 19878984, 18]-NRT-code)	[i]
5	Linear OOA(2²⁵³, 2839891, F₂, 8, 17) (dual of [(2839891, 8), 22718875, 18]-NRT-code)	[i]
6	Digital (236, 253, 2839891)-net over F₂	[i]