MinT - Information on Result #1079525

Information on Result #1079525

Linear OOA(2¹³⁶, 2097663, F₂, 4, 11) (dual of [(2097663, 4), 8390516, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁰, 513, F₂, 4, 5) (dual of [(513, 4), 2032, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 20, 513)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [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(2¹⁸⁰, 4194816, F₂, 4, 11) (dual of [(4194816, 4), 16779084, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁸², 4195326, F₂, 4, 11) (dual of [(4195326, 4), 16781122, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹³⁶, 2097663, F₂, 5, 11) (dual of [(2097663, 5), 10488179, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹³⁶, 2097663, F₂, 6, 11) (dual of [(2097663, 6), 12585842, 12]-NRT-code)	[i]
5	Linear OOA(2¹³⁶, 2097663, F₂, 7, 11) (dual of [(2097663, 7), 14683505, 12]-NRT-code)	[i]
6	Linear OOA(2¹³⁶, 2097663, F₂, 8, 11) (dual of [(2097663, 8), 16781168, 12]-NRT-code)	[i]
7	Digital (125, 136, 2097663)-net over F₂	[i]