MinT - Information on Result #945415

Information on Result #945415

Linear OOA(2⁷⁷, 682, F₂, 3, 14) (dual of [(682, 3), 1969, 15]-NRT-code), using OOA 3-folding based on linear OA(2⁷⁷, 2046, F₂, 14) (dual of [2046, 1969, 15]-code), using

discarding factors / shortening the dual code based on linear OA(2⁷⁷, 2047, F₂, 14) (dual of [2047, 1970, 15]-code), using
- 1 times truncation [i] based on linear OA(2⁷⁸, 2048, F₂, 15) (dual of [2048, 1970, 16]-code), using
  - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2⁷⁷, 682, F₂, 4, 14) (dual of [(682, 4), 2651, 15]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁷⁷, 682, F₂, 5, 14) (dual of [(682, 5), 3333, 15]-NRT-code)	[i]
3	Linear OOA(2⁷⁷, 682, F₂, 6, 14) (dual of [(682, 6), 4015, 15]-NRT-code)	[i]
4	Linear OOA(2⁷⁷, 682, F₂, 7, 14) (dual of [(682, 7), 4697, 15]-NRT-code)	[i]
5	Linear OOA(2⁷⁷, 682, F₂, 8, 14) (dual of [(682, 8), 5379, 15]-NRT-code)	[i]
6	Digital (63, 77, 682)-net over F₂	[i]