MinT - Information on Result #1079339

Information on Result #1079339

Linear OOA(2¹⁰⁵, 2097215, F₂, 4, 9) (dual of [(2097215, 4), 8388755, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹², 65, F₂, 4, 4) (dual of [(65, 4), 248, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2¹², 65, F₂, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (8, 12, 65)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2⁹³, 2097150, F₂, 4, 9) (dual of [(2097150, 4), 8388507, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁹³, 8388600, F₂, 9) (dual of [8388600, 8388507, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴⁷, 4194366, F₂, 4, 9) (dual of [(4194366, 4), 16777317, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁴⁹, 4194430, F₂, 4, 9) (dual of [(4194430, 4), 16777571, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹⁰⁵, 2097214, F₂, 5, 9) (dual of [(2097214, 5), 10485965, 10]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(2¹⁰⁵, 2097214, F₂, 6, 9) (dual of [(2097214, 6), 12583179, 10]-NRT-code)	[i]
5	Linear OOA(2¹⁰⁵, 2097214, F₂, 7, 9) (dual of [(2097214, 7), 14680393, 10]-NRT-code)	[i]
6	Linear OOA(2¹⁰⁵, 2097214, F₂, 8, 9) (dual of [(2097214, 8), 16777607, 10]-NRT-code)	[i]