MinT - Information on Result #1053999

Information on Result #1053999

Linear OOA(2²²¹, 2047, F₂, 4, 34) (dual of [(2047, 4), 7967, 35]-NRT-code), using OOA 4-folding based on linear OA(2²²¹, 8188, F₂, 34) (dual of [8188, 7967, 35]-code), using

discarding factors / shortening the dual code based on linear OA(2²²¹, 8191, F₂, 34) (dual of [8191, 7970, 35]-code), using
- 1 times truncation [i] based on linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using
  - an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²¹, 2046, F₂, 5, 34) (dual of [(2046, 5), 10009, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²¹, 2046, F₂, 6, 34) (dual of [(2046, 6), 12055, 35]-NRT-code)	[i]
3	Linear OOA(2²²¹, 2046, F₂, 7, 34) (dual of [(2046, 7), 14101, 35]-NRT-code)	[i]
4	Linear OOA(2²²¹, 2046, F₂, 8, 34) (dual of [(2046, 8), 16147, 35]-NRT-code)	[i]
5	Digital (187, 221, 2046)-net over F₂	[i]