MinT - Information on Result #808796

Information on Result #808796

Linear OOA(2²³¹, 1023, F₂, 2, 42) (dual of [(1023, 2), 1815, 43]-NRT-code), using OOA 2-folding based on linear OA(2²³¹, 2046, F₂, 42) (dual of [2046, 1815, 43]-code), using

discarding factors / shortening the dual code based on linear OA(2²³¹, 2047, F₂, 42) (dual of [2047, 1816, 43]-code), using
- 1 times truncation [i] based on linear OA(2²³², 2048, F₂, 43) (dual of [2048, 1816, 44]-code), using
  - an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [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(2²³¹, 846, F₂, 3, 42) (dual of [(846, 3), 2307, 43]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³¹, 846, F₂, 4, 42) (dual of [(846, 4), 3153, 43]-NRT-code)	[i]
3	Linear OOA(2²³¹, 846, F₂, 5, 42) (dual of [(846, 5), 3999, 43]-NRT-code)	[i]
4	Linear OOA(2²³¹, 846, F₂, 6, 42) (dual of [(846, 6), 4845, 43]-NRT-code)	[i]
5	Linear OOA(2²³¹, 846, F₂, 7, 42) (dual of [(846, 7), 5691, 43]-NRT-code)	[i]
6	Linear OOA(2²³¹, 846, F₂, 8, 42) (dual of [(846, 8), 6537, 43]-NRT-code)	[i]
7	Digital (189, 231, 846)-net over F₂	[i]