MinT - Information on Result #1616068

Information on Result #1616068

Linear OOA(2²¹⁶, 2097278, F₂, 4, 16) (dual of [(2097278, 4), 8388896, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³², 128, F₂, 4, 8) (dual of [(128, 4), 480, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³², 128, F₂, 2, 8) (dual of [(128, 2), 224, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2³², 256, F₂, 8) (dual of [256, 224, 9]-code), using
    - 1 times truncation [i] based on linear OA(2³³, 257, F₂, 9) (dual of [257, 224, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 257Â | 2¹⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
linear OOA(2¹⁸⁴, 2097150, F₂, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁶, 2097278, F₂, 5, 16) (dual of [(2097278, 5), 10486174, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁶, 2097278, F₂, 6, 16) (dual of [(2097278, 6), 12583452, 17]-NRT-code)	[i]
3	Linear OOA(2²¹⁶, 2097278, F₂, 7, 16) (dual of [(2097278, 7), 14680730, 17]-NRT-code)	[i]
4	Linear OOA(2²¹⁶, 2097278, F₂, 8, 16) (dual of [(2097278, 8), 16778008, 17]-NRT-code)	[i]
5	Digital (200, 216, 2097278)-net over F₂	[i]