MinT - Information on Result #1115954

Information on Result #1115954

Linear OOA(2²⁰⁶, 1677759, F₂, 5, 17) (dual of [(1677759, 5), 8388589, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 39, F₂, 5, 8) (dual of [(39, 5), 174, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
  - linear code embedding found in a computer search [i]
linear OOA(2¹⁸⁵, 1677720, F₂, 5, 17) (dual of [(1677720, 5), 8388415, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
  - discarding factors / shortening the dual code 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(2²⁰⁶, 1677759, F₂, 5, 16) (dual of [(1677759, 5), 8388589, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁷, 1677759, F₂, 5, 17) (dual of [(1677759, 5), 8388588, 18]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁸, 1677759, F₂, 5, 17) (dual of [(1677759, 5), 8388587, 18]-NRT-code)	[i]
4	Linear OOA(2²⁰⁹, 1677759, F₂, 5, 17) (dual of [(1677759, 5), 8388586, 18]-NRT-code)	[i]
5	Linear OOA(2²⁰⁶, 1554708, F₂, 6, 17) (dual of [(1554708, 6), 9328042, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
6	Linear OOA(2²⁰⁶, 1554708, F₂, 7, 17) (dual of [(1554708, 7), 10882750, 18]-NRT-code)	[i]
7	Linear OOA(2²⁰⁶, 1554708, F₂, 8, 17) (dual of [(1554708, 8), 12437458, 18]-NRT-code)	[i]
8	Digital (189, 206, 1554708)-net over F₂	[i]