MinT - Information on Result #1143417

Information on Result #1143417

Linear OOA(2¹⁹⁰, 1529171, F₂, 6, 12) (dual of [(1529171, 6), 9174836, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵², 131071, F₂, 6, 6) (dual of [(131071, 6), 786374, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁵², 131071, F₂, 5, 6) (dual of [(131071, 5), 655303, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
    - 1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹³⁸, 1398100, F₂, 6, 12) (dual of [(1398100, 6), 8388462, 13]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁹², 1529171, F₂, 6, 12) (dual of [(1529171, 6), 9174834, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁹⁰, 1529170, F₂, 7, 12) (dual of [(1529170, 7), 10704000, 13]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(2¹⁹⁰, 1529170, F₂, 8, 12) (dual of [(1529170, 8), 12233170, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁰, 1529170, F₂, 18, 12) (dual of [(1529170, 18), 27524870, 13]-NRT-code)	[i]