MinT - Information on Result #1079967

Information on Result #1079967

Linear OOA(2¹⁹⁹, 2099198, F₂, 4, 15) (dual of [(2099198, 4), 8396593, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁵, 2047, F₂, 4, 7) (dual of [(2047, 4), 8153, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 35, 2047)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶⁴, 2097151, F₂, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁶⁴, 4194302, F₂, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁹⁹, 2099198, F₂, 5, 15) (dual of [(2099198, 5), 10495791, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹⁹, 2099198, F₂, 6, 15) (dual of [(2099198, 6), 12594989, 16]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁹, 2099198, F₂, 7, 15) (dual of [(2099198, 7), 14694187, 16]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁹, 2099198, F₂, 8, 15) (dual of [(2099198, 8), 16793385, 16]-NRT-code)	[i]
5	Digital (184, 199, 2099198)-net over F₂	[i]