MinT - Information on Result #1131470

Information on Result #1131470

Linear OOA(2¹⁸⁸, 1398101, F₂, 6, 17) (dual of [(1398101, 6), 8388418, 18]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁸⁸, 2796202, F₂, 3, 17) (dual of [(2796202, 3), 8388418, 18]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on 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.

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		Method
1	Linear OOA(2¹⁸⁸, 1398101, F₂, 6, 16) (dual of [(1398101, 6), 8388418, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁸⁹, 1398101, F₂, 6, 17) (dual of [(1398101, 6), 8388417, 18]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁰, 1398101, F₂, 6, 17) (dual of [(1398101, 6), 8388416, 18]-NRT-code)	[i]
4	Linear OOA(2¹⁹¹, 1398101, F₂, 6, 17) (dual of [(1398101, 6), 8388415, 18]-NRT-code)	[i]
5	Linear OOA(2¹⁹², 1398101, F₂, 6, 17) (dual of [(1398101, 6), 8388414, 18]-NRT-code)	[i]
6	Linear OOA(2²⁰⁹, 1398140, F₂, 6, 17) (dual of [(1398140, 6), 8388631, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(2²²⁰, 1398179, F₂, 6, 17) (dual of [(1398179, 6), 8388854, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
8	Linear OOA(2¹⁸⁸, 1363697, F₂, 7, 17) (dual of [(1363697, 7), 9545691, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
9	Linear OOA(2¹⁸⁸, 1363697, F₂, 8, 17) (dual of [(1363697, 8), 10909388, 18]-NRT-code)	[i]
10	Digital (171, 188, 1363697)-net over F₂	[i]