MinT - Information on Result #946913

Information on Result #946913

Linear OOA(2¹⁶⁸, 1365, F₂, 3, 28) (dual of [(1365, 3), 3927, 29]-NRT-code), using OOA 3-folding based on linear OA(2¹⁶⁸, 4095, F₂, 28) (dual of [4095, 3927, 29]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁶⁸, 4096, F₂, 28) (dual of [4096, 3928, 29]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶⁹, 4097, F₂, 29) (dual of [4097, 3928, 30]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [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(2¹⁶⁸, 1116, F₂, 4, 28) (dual of [(1116, 4), 4296, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁸, 1116, F₂, 5, 28) (dual of [(1116, 5), 5412, 29]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁸, 1116, F₂, 6, 28) (dual of [(1116, 6), 6528, 29]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁸, 1116, F₂, 7, 28) (dual of [(1116, 7), 7644, 29]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁸, 1116, F₂, 8, 28) (dual of [(1116, 8), 8760, 29]-NRT-code)	[i]
6	Digital (140, 168, 1116)-net over F₂	[i]