MinT - Information on Result #1159799

Information on Result #1159799

Linear OOA(2²²⁷, 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776967, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 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(2²²⁷, 2396742, F₂, 7, 14) (dual of [(2396742, 7), 16776967, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²⁸, 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776966, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²²⁹, 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776965, 16]-NRT-code)	[i]
4	Linear OOA(2²³⁰, 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776964, 16]-NRT-code)	[i]
5	Linear OOA(2²³¹, 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776963, 16]-NRT-code)	[i]
6	Linear OOA(2²³², 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776962, 16]-NRT-code)	[i]
7	Linear OOA(2²³³, 2396742, F₂, 7, 15) (dual of [(2396742, 7), 16776961, 16]-NRT-code)	[i]
8	Linear OOA(2²²⁷, 2396741, F₂, 8, 15) (dual of [(2396741, 8), 19173701, 16]-NRT-code)	[i]	OOA Stacking with Additional Row
9	Linear OOA(2²²⁷, 2396741, F₂, 21, 15) (dual of [(2396741, 21), 50331334, 16]-NRT-code)	[i]	OOA Stacking with Additional Row