MinT - Information on Result #1106833

Information on Result #1106833

Linear OOA(256³⁹, 13107, F₂₅₆, 5, 20) (dual of [(13107, 5), 65496, 21]-NRT-code), using OOA 5-folding based on linear OA(256³⁹, 65535, F₂₅₆, 20) (dual of [65535, 65496, 21]-code), using

discarding factors / shortening the dual code based on linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using
- an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(256⁴⁹, 13364, F₂₅₆, 5, 20) (dual of [(13364, 5), 66771, 21]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(256⁵⁰, 13365, F₂₅₆, 5, 20) (dual of [(13365, 5), 66775, 21]-NRT-code)	[i]
3	Linear OOA(256⁵¹, 13366, F₂₅₆, 5, 20) (dual of [(13366, 5), 66779, 21]-NRT-code)	[i]
4	Linear OOA(256⁵², 13367, F₂₅₆, 5, 20) (dual of [(13367, 5), 66783, 21]-NRT-code)	[i]
5	Linear OOA(256⁵³, 13368, F₂₅₆, 5, 20) (dual of [(13368, 5), 66787, 21]-NRT-code)	[i]
6	Linear OOA(256⁵⁴, 13621, F₂₅₆, 5, 20) (dual of [(13621, 5), 68051, 21]-NRT-code)	[i]
7	Linear OOA(256⁵⁵, 13622, F₂₅₆, 5, 20) (dual of [(13622, 5), 68055, 21]-NRT-code)	[i]
8	Linear OOA(256⁵⁶, 13623, F₂₅₆, 5, 20) (dual of [(13623, 5), 68059, 21]-NRT-code)	[i]
9	Linear OOA(256⁵⁷, 13624, F₂₅₆, 5, 20) (dual of [(13624, 5), 68063, 21]-NRT-code)	[i]
10	Linear OOA(256⁵⁷, 13878, F₂₅₆, 5, 20) (dual of [(13878, 5), 69333, 21]-NRT-code)	[i]
11	Linear OOA(256³⁹, 13107, F₂₅₆, 6, 20) (dual of [(13107, 6), 78603, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
12	Digital (19, 39, 13107)-net over F₂₅₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound