MinT - Information on Result #1079512

Information on Result #1079512

Linear OOA(2¹²³, 2097157, F₂, 4, 11) (dual of [(2097157, 4), 8388505, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷, 7, F₂, 4, 5) (dual of [(7, 4), 21, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 7, 7)-net over F₂, using
  - a shift-net [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(2¹⁶⁷, 4194310, F₂, 4, 11) (dual of [(4194310, 4), 16777073, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁶⁹, 4194314, F₂, 4, 11) (dual of [(4194314, 4), 16777087, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹²³, 2097157, F₂, 5, 11) (dual of [(2097157, 5), 10485662, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹²³, 2097157, F₂, 6, 11) (dual of [(2097157, 6), 12582819, 12]-NRT-code)	[i]
5	Linear OOA(2¹²³, 2097157, F₂, 7, 11) (dual of [(2097157, 7), 14679976, 12]-NRT-code)	[i]
6	Linear OOA(2¹²³, 2097157, F₂, 8, 11) (dual of [(2097157, 8), 16777133, 12]-NRT-code)	[i]
7	Digital (112, 123, 2097157)-net over F₂	[i]