MinT - Information on Result #1052292

Information on Result #1052292

Linear OOA(2²¹⁰, 2097151, F₂, 4, 19) (dual of [(2097151, 4), 8388394, 20]-NRT-code), using OOA 2-folding based on linear OOA(2²¹⁰, 4194302, F₂, 2, 19) (dual of [(4194302, 2), 8388394, 20]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2²⁰⁸, 4194301, F₂, 2, 19) (dual of [(4194301, 2), 8388394, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²⁰⁸, 8388602, F₂, 19) (dual of [8388602, 8388394, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(2²¹⁰, 2097151, F₂, 4, 18) (dual of [(2097151, 4), 8388394, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²¹⁴, 2097152, F₂, 4, 19) (dual of [(2097152, 4), 8388394, 20]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²¹¹, 2097151, F₂, 4, 19) (dual of [(2097151, 4), 8388393, 20]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²¹², 2097151, F₂, 4, 19) (dual of [(2097151, 4), 8388392, 20]-NRT-code)	[i]
5	Linear OOA(2²¹³, 2097151, F₂, 4, 19) (dual of [(2097151, 4), 8388391, 20]-NRT-code)	[i]
6	Linear OOA(2²³¹, 2097180, F₂, 4, 19) (dual of [(2097180, 4), 8388489, 20]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
7	Linear OOA(2²⁵⁶, 2097838, F₂, 4, 19) (dual of [(2097838, 4), 8391096, 20]-NRT-code)	[i]
8	Linear OOA(2²⁶⁰, 2098521, F₂, 4, 19) (dual of [(2098521, 4), 8393824, 20]-NRT-code)	[i]