MinT - Information on Result #2174797

Information on Result #2174797

There is no linear OA(2¹⁷⁸, 208, F₂, 84) (dual of [208, 30, 85]-code), because 1 times code embedding in larger space would yield linear OA(2¹⁷⁹, 209, F₂, 84) (dual of [209, 30, 85]-code), but

adding a parity check bit [i] would yield linear OA(2¹⁸⁰, 210, F₂, 85) (dual of [210, 30, 86]-code), but
- â€œBKâ€ bound on codes from Brouwerâ€™s database [i]

Mode: Bound (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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(2¹⁷⁹, 208, F₂, 2, 85) (dual of [(208, 2), 237, 86]-NRT-code)	[i]	m-Reduction for OOAs
2	No linear OOA(2¹⁸⁰, 208, F₂, 2, 86) (dual of [(208, 2), 236, 87]-NRT-code)	[i]
3	No linear OOA(2¹⁸¹, 208, F₂, 2, 87) (dual of [(208, 2), 235, 88]-NRT-code)	[i]
4	No linear OOA(2¹⁸², 208, F₂, 2, 88) (dual of [(208, 2), 234, 89]-NRT-code)	[i]
5	No linear OOA(2¹⁸³, 208, F₂, 2, 89) (dual of [(208, 2), 233, 90]-NRT-code)	[i]
6	No linear OOA(2¹⁸⁴, 208, F₂, 2, 90) (dual of [(208, 2), 232, 91]-NRT-code)	[i]
7	No linear OOA(2¹⁸⁵, 208, F₂, 2, 91) (dual of [(208, 2), 231, 92]-NRT-code)	[i]
8	No linear OOA(2¹⁷⁸, 208, F₂, 2, 84) (dual of [(208, 2), 238, 85]-NRT-code)	[i]	Depth Reduction
9	No linear OOA(2¹⁷⁸, 208, F₂, 3, 84) (dual of [(208, 3), 446, 85]-NRT-code)	[i]
10	No linear OOA(2¹⁷⁸, 208, F₂, 4, 84) (dual of [(208, 4), 654, 85]-NRT-code)	[i]
11	No linear OOA(2¹⁷⁸, 208, F₂, 5, 84) (dual of [(208, 5), 862, 85]-NRT-code)	[i]
12	No linear OOA(2¹⁷⁸, 208, F₂, 6, 84) (dual of [(208, 6), 1070, 85]-NRT-code)	[i]
13	No linear OOA(2¹⁷⁸, 208, F₂, 7, 84) (dual of [(208, 7), 1278, 85]-NRT-code)	[i]
14	No linear OOA(2¹⁷⁸, 208, F₂, 8, 84) (dual of [(208, 8), 1486, 85]-NRT-code)	[i]
15	No digital (94, 178, 208)-net over F₂	[i]	Extracting Embedded Orthogonal Array