MinT - Information on Result #1175439

Information on Result #1175439

Linear OOA(2¹⁵⁹, 1398227, F₂, 8, 12) (dual of [(1398227, 8), 11185657, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 127, F₂, 8, 6) (dual of [(127, 8), 995, 7]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2²¹, 127, F₂, 6, 6) (dual of [(127, 6), 741, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(2²¹, 127, F₂, 5, 6) (dual of [(127, 5), 614, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2¹³⁸, 1398100, F₂, 8, 12) (dual of [(1398100, 8), 11184662, 13]-NRT-code), using
- OA 6-folding and stacking [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		This result only	Method
1	Linear OOA(2¹⁶¹, 1398227, F₂, 8, 12) (dual of [(1398227, 8), 11185655, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²²³, 2796454, F₂, 8, 12) (dual of [(2796454, 8), 22371409, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs