MinT - Information on Result #894217

Information on Result #894217

Linear OOA(2²⁰⁰, 5242876, F₂, 2, 13) (dual of [(5242876, 2), 10485552, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶¹, 1048575, F₂, 2, 6) (dual of [(1048575, 2), 2097089, 7]-NRT-code), using
- OOAs constructed from BCH codes [i]
linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁰, 5242876, F₂, 2, 12) (dual of [(5242876, 2), 10485552, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰², 5242877, F₂, 2, 13) (dual of [(5242877, 2), 10485552, 14]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²⁰¹, 5242876, F₂, 2, 13) (dual of [(5242876, 2), 10485551, 14]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁰⁰, 4133984, F₂, 3, 13) (dual of [(4133984, 3), 12401752, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2²⁰⁰, 4133984, F₂, 4, 13) (dual of [(4133984, 4), 16535736, 14]-NRT-code)	[i]
6	Linear OOA(2²⁰⁰, 4133984, F₂, 5, 13) (dual of [(4133984, 5), 20669720, 14]-NRT-code)	[i]
7	Linear OOA(2²⁰⁰, 4133984, F₂, 6, 13) (dual of [(4133984, 6), 24803704, 14]-NRT-code)	[i]
8	Linear OOA(2²⁰⁰, 4133984, F₂, 7, 13) (dual of [(4133984, 7), 28937688, 14]-NRT-code)	[i]
9	Linear OOA(2²⁰⁰, 4133984, F₂, 8, 13) (dual of [(4133984, 8), 33071672, 14]-NRT-code)	[i]
10	Digital (187, 200, 4133984)-net over F₂	[i]
11	Linear OOA(2²⁰⁰, 2621438, F₂, 4, 13) (dual of [(2621438, 4), 10485552, 14]-NRT-code)	[i]	OOA Folding