MinT - Information on Result #946906

Information on Result #946906

Linear OOA(2¹⁵⁴, 682, F₂, 3, 28) (dual of [(682, 3), 1892, 29]-NRT-code), using OOA 3-folding based on linear OA(2¹⁵⁴, 2046, F₂, 28) (dual of [2046, 1892, 29]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁵⁴, 2048, F₂, 28) (dual of [2048, 1894, 29]-code), using
- 1 times truncation [i] based on linear OA(2¹⁵⁵, 2049, F₂, 29) (dual of [2049, 1894, 30]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’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(2¹⁵⁴, 682, F₂, 4, 28) (dual of [(682, 4), 2574, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁵⁴, 682, F₂, 5, 28) (dual of [(682, 5), 3256, 29]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁴, 682, F₂, 6, 28) (dual of [(682, 6), 3938, 29]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁴, 682, F₂, 7, 28) (dual of [(682, 7), 4620, 29]-NRT-code)	[i]
5	Linear OOA(2¹⁵⁴, 682, F₂, 8, 28) (dual of [(682, 8), 5302, 29]-NRT-code)	[i]
6	Digital (126, 154, 682)-net over F₂	[i]