MinT - Information on Result #1234961

Information on Result #1234961

Linear OOA(2¹⁸⁴, 2129916, F₂, 4, 12) (dual of [(2129916, 4), 8519480, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 32766, F₂, 4, 6) (dual of [(32766, 4), 131018, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (40, 46, 32766)-net over F₂, using
  - 1 times m-reduction [i] based on digital (40, 47, 32766)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2⁴⁷, 32766, F₂, 7, 7) (dual of [(32766, 7), 229315, 8]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2⁴⁷, 32767, F₂, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-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		This result only	Method
1	Linear OOA(2²⁴⁸, 4227066, F₂, 4, 12) (dual of [(4227066, 4), 16908016, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs