MinT - Information on Result #1079760

Information on Result #1079760

Linear OOA(2¹⁶², 2097278, F₂, 4, 13) (dual of [(2097278, 4), 8388950, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 127, F₂, 4, 6) (dual of [(127, 4), 487, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
  - linear code embedding found in a computer search [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		Method
1	Linear OOA(2²²⁹, 4194556, F₂, 4, 13) (dual of [(4194556, 4), 16777995, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁶², 2097278, F₂, 5, 13) (dual of [(2097278, 5), 10486228, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁶², 2097278, F₂, 6, 13) (dual of [(2097278, 6), 12583506, 14]-NRT-code)	[i]
4	Linear OOA(2¹⁶², 2097278, F₂, 7, 13) (dual of [(2097278, 7), 14680784, 14]-NRT-code)	[i]
5	Linear OOA(2¹⁶², 2097278, F₂, 8, 13) (dual of [(2097278, 8), 16778062, 14]-NRT-code)	[i]
6	Digital (149, 162, 2097278)-net over F₂	[i]