MinT - Information on Result #1052638

Information on Result #1052638

Linear OOA(2¹⁴³, 2047, F₂, 4, 22) (dual of [(2047, 4), 8045, 23]-NRT-code), using OOA 4-folding based on linear OA(2¹⁴³, 8188, F₂, 22) (dual of [8188, 8045, 23]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁴³, 8191, F₂, 22) (dual of [8191, 8048, 23]-code), using
- 1 times truncation [i] based on linear OA(2¹⁴⁴, 8192, F₂, 23) (dual of [8192, 8048, 24]-code), using
  - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2¹⁴³, 2047, F₂, 5, 22) (dual of [(2047, 5), 10092, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁴³, 2047, F₂, 6, 22) (dual of [(2047, 6), 12139, 23]-NRT-code)	[i]
3	Linear OOA(2¹⁴³, 2047, F₂, 7, 22) (dual of [(2047, 7), 14186, 23]-NRT-code)	[i]
4	Linear OOA(2¹⁴³, 2047, F₂, 8, 22) (dual of [(2047, 8), 16233, 23]-NRT-code)	[i]
5	Digital (121, 143, 2047)-net over F₂	[i]