MinT - Information on Result #1051236

Information on Result #1051236

Linear OOA(2¹¹⁷, 2097151, F₂, 4, 10) (dual of [(2097151, 4), 8388487, 11]-NRT-code), using OOA 2-folding based on linear OOA(2¹¹⁷, 4194302, F₂, 2, 10) (dual of [(4194302, 2), 8388487, 11]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2¹¹⁵, 4194301, F₂, 2, 10) (dual of [(4194301, 2), 8388487, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹¹⁵, 8388602, F₂, 10) (dual of [8388602, 8388487, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹⁵, large, F₂, 10) (dual of [large, large−115, 11]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(2¹¹⁹, 2097151, F₂, 4, 10) (dual of [(2097151, 4), 8388485, 11]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹¹⁷, 2097151, F₂, 5, 10) (dual of [(2097151, 5), 10485638, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹¹⁷, 2097151, F₂, 6, 10) (dual of [(2097151, 6), 12582789, 11]-NRT-code)	[i]
4	Linear OOA(2¹¹⁷, 2097151, F₂, 7, 10) (dual of [(2097151, 7), 14679940, 11]-NRT-code)	[i]
5	Linear OOA(2¹¹⁷, 2097151, F₂, 8, 10) (dual of [(2097151, 8), 16777091, 11]-NRT-code)	[i]
6	Digital (107, 117, 2097151)-net over F₂	[i]