MinT - Information on Result #945784

Information on Result #945784

Linear OOA(2⁹⁹, 682, F₂, 3, 18) (dual of [(682, 3), 1947, 19]-NRT-code), using OOA 3-folding based on linear OA(2⁹⁹, 2046, F₂, 18) (dual of [2046, 1947, 19]-code), using

discarding factors / shortening the dual code based on linear OA(2⁹⁹, 2047, F₂, 18) (dual of [2047, 1948, 19]-code), using
- 1 times truncation [i] based on linear OA(2¹⁰⁰, 2048, F₂, 19) (dual of [2048, 1948, 20]-code), using
  - an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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		This result only	Method
1	Linear OOA(2⁹⁹, 681, F₂, 4, 18) (dual of [(681, 4), 2625, 19]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁹⁹, 681, F₂, 5, 18) (dual of [(681, 5), 3306, 19]-NRT-code)	[i]
3	Linear OOA(2⁹⁹, 681, F₂, 6, 18) (dual of [(681, 6), 3987, 19]-NRT-code)	[i]
4	Linear OOA(2⁹⁹, 681, F₂, 7, 18) (dual of [(681, 7), 4668, 19]-NRT-code)	[i]
5	Linear OOA(2⁹⁹, 681, F₂, 8, 18) (dual of [(681, 8), 5349, 19]-NRT-code)	[i]
6	Digital (81, 99, 681)-net over F₂	[i]