MinT - Information on Result #1159784

Information on Result #1159784

Linear OOA(2¹⁸³, 1198435, F₂, 7, 15) (dual of [(1198435, 7), 8388862, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 64, F₂, 7, 7) (dual of [(64, 7), 427, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(2²¹, 64, F₂, 6, 7) (dual of [(64, 6), 363, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (14, 21, 64)-net over F₂, using
    - linear code embedding found in a computer search [i]
linear OOA(2¹⁶², 1198371, F₂, 7, 15) (dual of [(1198371, 7), 8388435, 16]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2¹⁶², 8388597, F₂, 15) (dual of [8388597, 8388435, 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(2¹⁸³, 1198435, F₂, 7, 14) (dual of [(1198435, 7), 8388862, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁸⁴, 1198435, F₂, 7, 15) (dual of [(1198435, 7), 8388861, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁸, 2396870, F₂, 7, 15) (dual of [(2396870, 7), 16777842, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
4	Linear OOA(2¹⁸³, 1198434, F₂, 8, 15) (dual of [(1198434, 8), 9587289, 16]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2¹⁸³, 1198434, F₂, 21, 15) (dual of [(1198434, 21), 25166931, 16]-NRT-code)	[i]	OOA Stacking with Additional Row