MinT - Information on Result #1079763

Information on Result #1079763

Linear OOA(2¹⁹³, 2228222, F₂, 4, 13) (dual of [(2228222, 4), 8912695, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵², 131071, F₂, 4, 6) (dual of [(131071, 4), 524232, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
  - 1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁴¹, 2097151, F₂, 4, 13) (dual of [(2097151, 4), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴¹, 4194302, F₂, 2, 13) (dual of [(4194302, 2), 8388463, 14]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 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(2²⁶⁰, 4456444, F₂, 4, 13) (dual of [(4456444, 4), 17825516, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁵⁷, 4325372, F₂, 4, 13) (dual of [(4325372, 4), 17301231, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs