MinT - Information on Result #1079952

Information on Result #1079952

Linear OOA(2¹⁹⁷, 2099197, F₂, 4, 15) (dual of [(2099197, 4), 8396591, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁵, 2047, F₂, 4, 7) (dual of [(2047, 4), 8153, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 35, 2047)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶², 2097150, F₂, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁹⁷, 2099197, F₂, 4, 14) (dual of [(2099197, 4), 8396591, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁹⁸, 2099197, F₂, 4, 15) (dual of [(2099197, 4), 8396590, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁷, 2099197, F₂, 5, 15) (dual of [(2099197, 5), 10495788, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁹⁷, 2099197, F₂, 6, 15) (dual of [(2099197, 6), 12594985, 16]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁷, 2099197, F₂, 7, 15) (dual of [(2099197, 7), 14694182, 16]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁷, 2099197, F₂, 8, 15) (dual of [(2099197, 8), 16793379, 16]-NRT-code)	[i]
7	Digital (182, 197, 2099197)-net over F₂	[i]