MinT - Information on Result #894254

Information on Result #894254

Linear OOA(2²¹⁴, 4325372, F₂, 2, 14) (dual of [(4325372, 2), 8650530, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵³, 131071, F₂, 2, 7) (dual of [(131071, 2), 262089, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (46, 53, 131071)-net over F₂, using
  - nets constructed from net-embeddable 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(2²¹⁶, 4325373, F₂, 2, 14) (dual of [(4325373, 2), 8650530, 15]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²¹⁴, 3109432, F₂, 3, 14) (dual of [(3109432, 3), 9328082, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²¹⁴, 3109432, F₂, 4, 14) (dual of [(3109432, 4), 12437514, 15]-NRT-code)	[i]
4	Linear OOA(2²¹⁴, 3109432, F₂, 5, 14) (dual of [(3109432, 5), 15546946, 15]-NRT-code)	[i]
5	Linear OOA(2²¹⁴, 3109432, F₂, 6, 14) (dual of [(3109432, 6), 18656378, 15]-NRT-code)	[i]
6	Linear OOA(2²¹⁴, 3109432, F₂, 7, 14) (dual of [(3109432, 7), 21765810, 15]-NRT-code)	[i]
7	Linear OOA(2²¹⁴, 3109432, F₂, 8, 14) (dual of [(3109432, 8), 24875242, 15]-NRT-code)	[i]
8	Digital (200, 214, 3109432)-net over F₂	[i]
9	Linear OOA(2²¹⁴, 2162686, F₂, 4, 14) (dual of [(2162686, 4), 8650530, 15]-NRT-code)	[i]	OOA Folding