MinT - Information on Result #894258

Information on Result #894258

Linear OOA(2²²⁶, 6291452, F₂, 2, 14) (dual of [(6291452, 2), 12582678, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097151, F₂, 2, 7) (dual of [(2097151, 2), 4194237, 8]-NRT-code), using
- OOAs constructed from BCH codes [i]
linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²⁸, 6291453, F₂, 2, 14) (dual of [(6291453, 2), 12582678, 15]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²²⁶, 6291452, F₂, 3, 14) (dual of [(6291452, 3), 18874130, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²²⁶, 6291452, F₂, 4, 14) (dual of [(6291452, 4), 25165582, 15]-NRT-code)	[i]
4	Linear OOA(2²²⁶, 6291452, F₂, 5, 14) (dual of [(6291452, 5), 31457034, 15]-NRT-code)	[i]
5	Linear OOA(2²²⁶, 6291452, F₂, 6, 14) (dual of [(6291452, 6), 37748486, 15]-NRT-code)	[i]
6	Linear OOA(2²²⁶, 6291452, F₂, 7, 14) (dual of [(6291452, 7), 44039938, 15]-NRT-code)	[i]
7	Linear OOA(2²²⁶, 6291452, F₂, 8, 14) (dual of [(6291452, 8), 50331390, 15]-NRT-code)	[i]
8	Digital (212, 226, 6291452)-net over F₂	[i]
9	Linear OOA(2²²⁶, 3145726, F₂, 3, 14) (dual of [(3145726, 3), 9436952, 15]-NRT-code)	[i]	OOA Folding
10	Linear OOA(2²²⁶, 3145726, F₂, 4, 14) (dual of [(3145726, 4), 12582678, 15]-NRT-code)	[i]	OOA Folding