MinT - Information on Result #894172

Information on Result #894172

Linear OOA(2¹⁷⁸, 4202492, F₂, 2, 12) (dual of [(4202492, 2), 8404806, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁰, 8191, F₂, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F₂, using
  - 1 times m-reduction [i] based on digital (34, 41, 8191)-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(2¹⁸⁰, 4202493, F₂, 2, 12) (dual of [(4202493, 2), 8404806, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁷⁸, 3195645, F₂, 3, 12) (dual of [(3195645, 3), 9586757, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁷⁸, 3195645, F₂, 4, 12) (dual of [(3195645, 4), 12782402, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁸, 3195645, F₂, 5, 12) (dual of [(3195645, 5), 15978047, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁸, 3195645, F₂, 6, 12) (dual of [(3195645, 6), 19173692, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁷⁸, 3195645, F₂, 7, 12) (dual of [(3195645, 7), 22369337, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁷⁸, 3195645, F₂, 8, 12) (dual of [(3195645, 8), 25564982, 13]-NRT-code)	[i]
8	Digital (166, 178, 3195645)-net over F₂	[i]
9	Linear OOA(2¹⁷⁸, 2101246, F₂, 4, 12) (dual of [(2101246, 4), 8404806, 13]-NRT-code)	[i]	OOA Folding