MinT - Information on Result #1159623

Information on Result #1159623

Linear OOA(2¹⁴⁹, 1398111, F₂, 7, 13) (dual of [(1398111, 7), 9786628, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰, 11, F₂, 7, 6) (dual of [(11, 7), 67, 7]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(2¹⁰, 11, F₂, 6, 6) (dual of [(11, 6), 56, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹⁰, 11, F₂, 5, 6) (dual of [(11, 5), 45, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 11)-net over F₂, using
      - 1 times m-reduction [i] based on digital (4, 11, 11)-net over F₂, using
        a shift-net [i]
linear OOA(2¹³⁹, 1398100, F₂, 7, 13) (dual of [(1398100, 7), 9786561, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2¹³⁹, 8388601, F₂, 13) (dual of [8388601, 8388462, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²¹³, 2796222, F₂, 7, 13) (dual of [(2796222, 7), 19573341, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs