MinT - Information on Result #1079851

Information on Result #1079851

Linear OOA(2¹⁸⁴, 2097277, F₂, 4, 14) (dual of [(2097277, 4), 8388924, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²³, 127, F₂, 4, 7) (dual of [(127, 4), 485, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 23, 127)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶¹, 2097150, F₂, 4, 14) (dual of [(2097150, 4), 8388439, 15]-NRT-code), using
- OOA 4-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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁴⁹, 4194427, F₂, 4, 14) (dual of [(4194427, 4), 16777459, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁵², 4194554, F₂, 4, 14) (dual of [(4194554, 4), 16777964, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹⁸⁴, 2097277, F₂, 5, 14) (dual of [(2097277, 5), 10486201, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁸⁴, 2097277, F₂, 6, 14) (dual of [(2097277, 6), 12583478, 15]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁴, 2097277, F₂, 7, 14) (dual of [(2097277, 7), 14680755, 15]-NRT-code)	[i]
6	Linear OOA(2¹⁸⁴, 2097277, F₂, 8, 14) (dual of [(2097277, 8), 16778032, 15]-NRT-code)	[i]
7	Digital (170, 184, 2097277)-net over F₂	[i]