MinT - Information on Result #1653575

Information on Result #1653575

Linear OOA(2²⁰⁸, 1677760, F₂, 5, 17) (dual of [(1677760, 5), 8388592, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²³, 40, F₂, 5, 8) (dual of [(40, 5), 177, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²³, 40, F₂, 2, 8) (dual of [(40, 2), 57, 9]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹, 39, F₂, 2, 8) (dual of [(39, 2), 57, 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁹, 1677760, F₂, 5, 17) (dual of [(1677760, 5), 8388591, 18]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁰⁸, 1677760, F₂, 6, 17) (dual of [(1677760, 6), 10066352, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²⁰⁸, 1677760, F₂, 7, 17) (dual of [(1677760, 7), 11744112, 18]-NRT-code)	[i]
4	Linear OOA(2²⁰⁸, 1677760, F₂, 8, 17) (dual of [(1677760, 8), 13421872, 18]-NRT-code)	[i]
5	Digital (191, 208, 1677760)-net over F₂	[i]