MinT - Information on Result #1079599

Information on Result #1079599

Linear OOA(2¹⁴⁸, 2097161, F₂, 4, 12) (dual of [(2097161, 4), 8388496, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰, 11, F₂, 4, 6) (dual of [(11, 4), 34, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 10, 11)-net over F₂, using
  - 1 times m-reduction [i] based on digital (4, 11, 11)-net over F₂, using
    - a shift-net [i]
linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁵, 4194322, F₂, 4, 12) (dual of [(4194322, 4), 16777073, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹², 4194311, F₂, 4, 12) (dual of [(4194311, 4), 16777032, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹⁴⁸, 2097161, F₂, 5, 12) (dual of [(2097161, 5), 10485657, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁴⁸, 2097161, F₂, 6, 12) (dual of [(2097161, 6), 12582818, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁸, 2097161, F₂, 7, 12) (dual of [(2097161, 7), 14679979, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁸, 2097161, F₂, 8, 12) (dual of [(2097161, 8), 16777140, 13]-NRT-code)	[i]
7	Digital (136, 148, 2097161)-net over F₂	[i]