MinT - Information on Result #1079261

Information on Result #1079261

Linear OOA(2¹¹², 2098175, F₂, 4, 8) (dual of [(2098175, 4), 8392588, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁰, 1025, F₂, 4, 4) (dual of [(1025, 4), 4080, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁰, 1025, F₂, 3, 4) (dual of [(1025, 3), 3055, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (16, 20, 1025)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2⁹², 2097150, F₂, 4, 8) (dual of [(2097150, 4), 8388508, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁹², 8388600, F₂, 8) (dual of [8388600, 8388508, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁵⁴, 4195326, F₂, 4, 8) (dual of [(4195326, 4), 16781150, 9]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁵⁵, 4195328, F₂, 4, 8) (dual of [(4195328, 4), 16781157, 9]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁶, 4196350, F₂, 4, 8) (dual of [(4196350, 4), 16785244, 9]-NRT-code)	[i]
4	Linear OOA(2¹¹², 2098174, F₂, 5, 8) (dual of [(2098174, 5), 10490758, 9]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2¹¹², 2098174, F₂, 6, 8) (dual of [(2098174, 6), 12588932, 9]-NRT-code)	[i]
6	Linear OOA(2¹¹², 2098174, F₂, 7, 8) (dual of [(2098174, 7), 14687106, 9]-NRT-code)	[i]
7	Linear OOA(2¹¹², 2098174, F₂, 8, 8) (dual of [(2098174, 8), 16785280, 9]-NRT-code)	[i]