MinT - Information on Result #1079515

Information on Result #1079515

Linear OOA(2¹²⁶, 2097170, F₂, 4, 11) (dual of [(2097170, 4), 8388554, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰, 20, F₂, 4, 5) (dual of [(20, 4), 70, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 10, 20)-net over F₂, using
  - linear code embedding found in a computer search [i]
linear OOA(2¹¹⁶, 2097150, F₂, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁷⁰, 4194323, F₂, 4, 11) (dual of [(4194323, 4), 16777122, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁷², 4194340, F₂, 4, 11) (dual of [(4194340, 4), 16777188, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹²⁶, 2097170, F₂, 5, 11) (dual of [(2097170, 5), 10485724, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹²⁶, 2097170, F₂, 6, 11) (dual of [(2097170, 6), 12582894, 12]-NRT-code)	[i]
5	Linear OOA(2¹²⁶, 2097170, F₂, 7, 11) (dual of [(2097170, 7), 14680064, 12]-NRT-code)	[i]
6	Linear OOA(2¹²⁶, 2097170, F₂, 8, 11) (dual of [(2097170, 8), 16777234, 12]-NRT-code)	[i]
7	Digital (115, 126, 2097170)-net over F₂	[i]