MinT - Information on Result #1009389

Information on Result #1009389

Linear OOA(2²³⁶, 2798931, F₂, 3, 16) (dual of [(2798931, 3), 8396557, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵², 2730, F₂, 3, 8) (dual of [(2730, 3), 8138, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁵², 8190, F₂, 8) (dual of [8190, 8138, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁵², 8192, F₂, 8) (dual of [8192, 8140, 9]-code), using
    - 1 times truncation [i] based on linear OA(2⁵³, 8193, F₂, 9) (dual of [8193, 8140, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’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(2²³⁶, 2798931, F₂, 4, 16) (dual of [(2798931, 4), 11195488, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁶, 2798931, F₂, 5, 16) (dual of [(2798931, 5), 13994419, 17]-NRT-code)	[i]
3	Linear OOA(2²³⁶, 2798931, F₂, 6, 16) (dual of [(2798931, 6), 16793350, 17]-NRT-code)	[i]
4	Linear OOA(2²³⁶, 2798931, F₂, 7, 16) (dual of [(2798931, 7), 19592281, 17]-NRT-code)	[i]
5	Linear OOA(2²³⁶, 2798931, F₂, 8, 16) (dual of [(2798931, 8), 22391212, 17]-NRT-code)	[i]
6	Digital (220, 236, 2798931)-net over F₂	[i]