MinT - Information on Result #1159786

Information on Result #1159786

Linear OOA(2¹⁸⁸, 1198625, F₂, 7, 15) (dual of [(1198625, 7), 8390187, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁶, 254, F₂, 7, 7) (dual of [(254, 7), 1752, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
  - OOAs constructed from BCH codes [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(2¹⁸⁸, 1198625, F₂, 7, 14) (dual of [(1198625, 7), 8390187, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁸⁹, 1198625, F₂, 7, 15) (dual of [(1198625, 7), 8390186, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁰, 1198625, F₂, 7, 15) (dual of [(1198625, 7), 8390185, 16]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁵³, 2397250, F₂, 7, 15) (dual of [(2397250, 7), 16780497, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(2¹⁸⁸, 1198624, F₂, 8, 15) (dual of [(1198624, 8), 9588804, 16]-NRT-code)	[i]	OOA Stacking with Additional Row
6	Linear OOA(2¹⁸⁸, 1198624, F₂, 21, 15) (dual of [(1198624, 21), 25170916, 16]-NRT-code)	[i]	OOA Stacking with Additional Row