MinT - Information on Result #1235005

Information on Result #1235005

Linear OOA(2¹⁸⁸, 2162684, F₂, 4, 13) (dual of [(2162684, 4), 8650548, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁹, 65534, F₂, 4, 6) (dual of [(65534, 4), 262087, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (43, 49, 65534)-net over F₂, using
  - 1 times m-reduction [i] based on digital (43, 50, 65534)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2⁵⁰, 65534, F₂, 7, 7) (dual of [(65534, 7), 458688, 8]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2⁵⁰, 65535, F₂, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 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(2²⁵², 4259834, F₂, 4, 13) (dual of [(4259834, 4), 17039084, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs