MinT - Information on Result #894176

Information on Result #894176

Linear OOA(2¹⁹⁰, 4325372, F₂, 2, 12) (dual of [(4325372, 2), 8650554, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵², 131071, F₂, 2, 6) (dual of [(131071, 2), 262090, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
  - 1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 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(2¹⁹², 4325373, F₂, 2, 12) (dual of [(4325373, 2), 8650554, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁹⁰, 4325372, F₂, 3, 12) (dual of [(4325372, 3), 12975926, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁹⁰, 4325372, F₂, 4, 12) (dual of [(4325372, 4), 17301298, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁰, 4325372, F₂, 5, 12) (dual of [(4325372, 5), 21626670, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁰, 4325372, F₂, 6, 12) (dual of [(4325372, 6), 25952042, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁰, 4325372, F₂, 7, 12) (dual of [(4325372, 7), 30277414, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁰, 4325372, F₂, 8, 12) (dual of [(4325372, 8), 34602786, 13]-NRT-code)	[i]
8	Digital (178, 190, 4325372)-net over F₂	[i]
9	Linear OOA(2¹⁹⁰, 2162686, F₂, 4, 12) (dual of [(2162686, 4), 8650554, 13]-NRT-code)	[i]	OOA Folding