MinT - Information on Result #1079344

Information on Result #1079344

Linear OOA(2¹¹¹, 2097661, F₂, 4, 9) (dual of [(2097661, 4), 8390533, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁸, 511, F₂, 4, 4) (dual of [(511, 4), 2026, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2¹⁸, 511, F₂, 3, 4) (dual of [(511, 3), 1515, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (14, 18, 511)-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(2¹⁵⁵, 4195322, F₂, 4, 9) (dual of [(4195322, 4), 16781133, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹¹¹, 2097660, F₂, 5, 9) (dual of [(2097660, 5), 10488189, 10]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(2¹¹¹, 2097660, F₂, 6, 9) (dual of [(2097660, 6), 12585849, 10]-NRT-code)	[i]
4	Linear OOA(2¹¹¹, 2097660, F₂, 7, 9) (dual of [(2097660, 7), 14683509, 10]-NRT-code)	[i]
5	Linear OOA(2¹¹¹, 2097660, F₂, 8, 9) (dual of [(2097660, 8), 16781169, 10]-NRT-code)	[i]