MinT - Information on Result #1080043

Information on Result #1080043

Linear OOA(2²⁰⁷, 2097190, F₂, 4, 16) (dual of [(2097190, 4), 8388553, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 39, F₂, 4, 8) (dual of [(39, 4), 135, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
  - linear code embedding found in a computer search [i]
linear OOA(2¹⁸⁶, 2097151, F₂, 4, 16) (dual of [(2097151, 4), 8388418, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁸⁶, 4194302, F₂, 2, 16) (dual of [(4194302, 2), 8388418, 17]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁴, 4194301, F₂, 2, 16) (dual of [(4194301, 2), 8388418, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁸⁴, 8388602, F₂, 16) (dual of [8388602, 8388418, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁷, 1763527, F₂, 5, 16) (dual of [(1763527, 5), 8817428, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰⁷, 1763527, F₂, 6, 16) (dual of [(1763527, 6), 10580955, 17]-NRT-code)	[i]
3	Linear OOA(2²⁰⁷, 1763527, F₂, 7, 16) (dual of [(1763527, 7), 12344482, 17]-NRT-code)	[i]
4	Linear OOA(2²⁰⁷, 1763527, F₂, 8, 16) (dual of [(1763527, 8), 14108009, 17]-NRT-code)	[i]
5	Digital (191, 207, 1763527)-net over F₂	[i]
6	Linear OOA(2²⁰⁷, 1048595, F₂, 8, 16) (dual of [(1048595, 8), 8388553, 17]-NRT-code)	[i]	OOA Folding