MinT - Information on Result #1009383

Information on Result #1009383

Linear OOA(2²²⁸, 2796883, F₂, 3, 16) (dual of [(2796883, 3), 8390421, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁴, 682, F₂, 3, 8) (dual of [(682, 3), 2002, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁴⁴, 2046, F₂, 8) (dual of [2046, 2002, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁴⁴, 2048, F₂, 8) (dual of [2048, 2004, 9]-code), using
    - 1 times truncation [i] based on linear OA(2⁴⁵, 2049, F₂, 9) (dual of [2049, 2004, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
linear OOA(2¹⁸⁴, 2796201, F₂, 3, 16) (dual of [(2796201, 3), 8388419, 17]-NRT-code), using
- OOA 3-folding [i] 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(2²²⁸, 2331689, F₂, 4, 16) (dual of [(2331689, 4), 9326528, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²⁸, 2331689, F₂, 5, 16) (dual of [(2331689, 5), 11658217, 17]-NRT-code)	[i]
3	Linear OOA(2²²⁸, 2331689, F₂, 6, 16) (dual of [(2331689, 6), 13989906, 17]-NRT-code)	[i]
4	Linear OOA(2²²⁸, 2331689, F₂, 7, 16) (dual of [(2331689, 7), 16321595, 17]-NRT-code)	[i]
5	Linear OOA(2²²⁸, 2331689, F₂, 8, 16) (dual of [(2331689, 8), 18653284, 17]-NRT-code)	[i]
6	Digital (212, 228, 2331689)-net over F₂	[i]