MinT - Information on Result #1079866

Information on Result #1079866

Linear OOA(2¹⁸⁶, 2097278, F₂, 4, 14) (dual of [(2097278, 4), 8388926, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²³, 127, F₂, 4, 7) (dual of [(127, 4), 485, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 23, 127)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶³, 2097151, F₂, 4, 14) (dual of [(2097151, 4), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁶³, 4194302, F₂, 2, 14) (dual of [(4194302, 2), 8388441, 15]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁴, 4194556, F₂, 4, 14) (dual of [(4194556, 4), 16777970, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁸⁶, 2097278, F₂, 5, 14) (dual of [(2097278, 5), 10486204, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁸⁶, 2097278, F₂, 6, 14) (dual of [(2097278, 6), 12583482, 15]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁶, 2097278, F₂, 7, 14) (dual of [(2097278, 7), 14680760, 15]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁶, 2097278, F₂, 8, 14) (dual of [(2097278, 8), 16778038, 15]-NRT-code)	[i]
6	Digital (172, 186, 2097278)-net over F₂	[i]