MinT - Information on Result #894174

Information on Result #894174

Linear OOA(2¹⁸⁴, 4227068, F₂, 2, 12) (dual of [(4227068, 2), 8453952, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 32767, F₂, 2, 6) (dual of [(32767, 2), 65488, 7]-NRT-code), using
- OOAs constructed from 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(2¹⁸⁶, 4227069, F₂, 2, 12) (dual of [(4227069, 2), 8453952, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁸⁴, 4227068, F₂, 3, 12) (dual of [(4227068, 3), 12681020, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁸⁴, 4227068, F₂, 4, 12) (dual of [(4227068, 4), 16908088, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁴, 4227068, F₂, 5, 12) (dual of [(4227068, 5), 21135156, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁴, 4227068, F₂, 6, 12) (dual of [(4227068, 6), 25362224, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁸⁴, 4227068, F₂, 7, 12) (dual of [(4227068, 7), 29589292, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁸⁴, 4227068, F₂, 8, 12) (dual of [(4227068, 8), 33816360, 13]-NRT-code)	[i]
8	Digital (172, 184, 4227068)-net over F₂	[i]
9	Linear OOA(2¹⁸⁴, 2113534, F₂, 4, 12) (dual of [(2113534, 4), 8453952, 13]-NRT-code)	[i]	OOA Folding