MinT - Information on Result #1175450

Information on Result #1175450

Linear OOA(2¹⁷⁸, 1406291, F₂, 8, 12) (dual of [(1406291, 8), 11250150, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁰, 8191, F₂, 8, 6) (dual of [(8191, 8), 65488, 7]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2⁴⁰, 8191, F₂, 6, 6) (dual of [(8191, 6), 49106, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁴⁰, 8191, F₂, 5, 6) (dual of [(8191, 5), 40915, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F₂, using
      - 1 times m-reduction [i] based on digital (34, 41, 8191)-net over F₂, using
        nets constructed from net-embeddable BCH codes [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(2¹⁸⁰, 1406291, F₂, 8, 12) (dual of [(1406291, 8), 11250148, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁴², 2812582, F₂, 8, 12) (dual of [(2812582, 8), 22500414, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs