MinT - Information on Result #1052010

Information on Result #1052010

Linear OOA(2¹⁸⁷, 2097151, F₂, 4, 17) (dual of [(2097151, 4), 8388417, 18]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁸⁷, 4194302, F₂, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 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.

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(2¹⁸⁷, 2097151, F₂, 4, 16) (dual of [(2097151, 4), 8388417, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁹¹, 2097152, F₂, 4, 17) (dual of [(2097152, 4), 8388417, 18]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2¹⁸⁸, 2097151, F₂, 4, 17) (dual of [(2097151, 4), 8388416, 18]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹⁸⁹, 2097151, F₂, 4, 17) (dual of [(2097151, 4), 8388415, 18]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁰, 2097151, F₂, 4, 17) (dual of [(2097151, 4), 8388414, 18]-NRT-code)	[i]
6	Linear OOA(2²⁰⁸, 2097190, F₂, 4, 17) (dual of [(2097190, 4), 8388552, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(2²¹⁹, 2097229, F₂, 4, 17) (dual of [(2097229, 4), 8388697, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs