MinT - Information on Result #1175804

Information on Result #1175804

Linear OOA(2²⁰⁶, 1048614, F₂, 8, 17) (dual of [(1048614, 8), 8388706, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 39, F₂, 8, 8) (dual of [(39, 8), 291, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2²¹, 39, F₂, 7, 8) (dual of [(39, 7), 252, 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, 1048575, F₂, 8, 17) (dual of [(1048575, 8), 8388415, 18]-NRT-code), using
- OOA 8-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, 1048614, F₂, 8, 16) (dual of [(1048614, 8), 8388706, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁷, 1048614, F₂, 8, 17) (dual of [(1048614, 8), 8388705, 18]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁸, 1048614, F₂, 8, 17) (dual of [(1048614, 8), 8388704, 18]-NRT-code)	[i]
4	Linear OOA(2²⁰⁹, 1048614, F₂, 8, 17) (dual of [(1048614, 8), 8388703, 18]-NRT-code)	[i]
5	Linear OOA(2²⁰⁶, 1048613, F₂, 24, 17) (dual of [(1048613, 24), 25166506, 18]-NRT-code)	[i]	OOA Stacking with Additional Row