MinT - Information on Result #1159797

Information on Result #1159797

Linear OOA(2²²¹, 1722658, F₂, 7, 15) (dual of [(1722658, 7), 12058385, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵⁹, 524287, F₂, 7, 7) (dual of [(524287, 7), 3669950, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁵⁹, 524287, F₂, 6, 7) (dual of [(524287, 6), 3145663, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (52, 59, 524287)-net over F₂, using
    - nets constructed from net-embeddable 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(2²²¹, 1722658, F₂, 7, 14) (dual of [(1722658, 7), 12058385, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²², 1722658, F₂, 7, 15) (dual of [(1722658, 7), 12058384, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²²³, 1722658, F₂, 7, 15) (dual of [(1722658, 7), 12058383, 16]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²²¹, 1722657, F₂, 8, 15) (dual of [(1722657, 8), 13781035, 16]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2²²¹, 1722657, F₂, 21, 15) (dual of [(1722657, 21), 36175576, 16]-NRT-code)	[i]	OOA Stacking with Additional Row