MinT - Information on Result #894177

Information on Result #894177

Linear OOA(2¹⁹³, 4456444, F₂, 2, 12) (dual of [(4456444, 2), 8912695, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵⁵, 262143, F₂, 2, 6) (dual of [(262143, 2), 524231, 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(2¹⁹⁵, 4456445, F₂, 2, 12) (dual of [(4456445, 2), 8912695, 13]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁹³, 4456444, F₂, 3, 12) (dual of [(4456444, 3), 13369139, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁹³, 4456444, F₂, 4, 12) (dual of [(4456444, 4), 17825583, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁹³, 4456444, F₂, 5, 12) (dual of [(4456444, 5), 22282027, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁹³, 4456444, F₂, 6, 12) (dual of [(4456444, 6), 26738471, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁹³, 4456444, F₂, 7, 12) (dual of [(4456444, 7), 31194915, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁹³, 4456444, F₂, 8, 12) (dual of [(4456444, 8), 35651359, 13]-NRT-code)	[i]
8	Digital (181, 193, 4456444)-net over F₂	[i]
9	Linear OOA(2¹⁹³, 2228222, F₂, 4, 12) (dual of [(2228222, 4), 8912695, 13]-NRT-code)	[i]	OOA Folding