MinT - Information on Result #2864855

Information on Result #2864855

Linear OOA(2¹⁶⁶, 1677721, F₂, 5, 14) (dual of [(1677721, 5), 8388439, 15]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁶¹, 1677720, F₂, 5, 14) (dual of [(1677720, 5), 8388439, 15]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁶¹, 8388600, F₂, 14) (dual of [8388600, 8388439, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2¹⁶⁷, 1677721, F₂, 5, 14) (dual of [(1677721, 5), 8388438, 15]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³¹, 3355442, F₂, 5, 14) (dual of [(3355442, 5), 16776979, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹⁶⁶, 1677721, F₂, 6, 14) (dual of [(1677721, 6), 10066160, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁶⁶, 1677721, F₂, 7, 14) (dual of [(1677721, 7), 11743881, 15]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁶, 1677721, F₂, 8, 14) (dual of [(1677721, 8), 13421602, 15]-NRT-code)	[i]
6	Digital (152, 166, 1677721)-net over F₂	[i]