MinT - Information on Result #548429

Information on Result #548429

There is no linear OA(2²⁵⁴, 278, F₂, 124) (dual of [278, 24, 125]-code), because residual code would yield linear OA(2¹³⁰, 153, F₂, 62) (dual of [153, 23, 63]-code), but

adding a parity check bit [i] would yield linear OA(2¹³¹, 154, F₂, 63) (dual of [154, 23, 64]-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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(2²⁵⁵, 279, F₂, 125) (dual of [279, 24, 126]-code)	[i]		Truncation
2	No linear OA(2²⁵⁶, 280, F₂, 126) (dual of [280, 24, 127]-code)	[i]
3	No linear OA(2²⁵⁷, 281, F₂, 127) (dual of [281, 24, 128]-code)	[i]
4	No linear OOA(2²⁵⁵, 278, F₂, 2, 125) (dual of [(278, 2), 301, 126]-NRT-code)	[i]		m-Reduction for OOAs
5	No linear OOA(2²⁵⁶, 278, F₂, 2, 126) (dual of [(278, 2), 300, 127]-NRT-code)	[i]
6	No linear OOA(2²⁵⁷, 278, F₂, 2, 127) (dual of [(278, 2), 299, 128]-NRT-code)	[i]
7	No linear OOA(2²⁵⁴, 278, F₂, 2, 124) (dual of [(278, 2), 302, 125]-NRT-code)	[i]		Depth Reduction
8	No linear OOA(2²⁵⁴, 278, F₂, 3, 124) (dual of [(278, 3), 580, 125]-NRT-code)	[i]
9	No linear OOA(2²⁵⁴, 278, F₂, 4, 124) (dual of [(278, 4), 858, 125]-NRT-code)	[i]
10	No linear OOA(2²⁵⁴, 278, F₂, 5, 124) (dual of [(278, 5), 1136, 125]-NRT-code)	[i]
11	No linear OOA(2²⁵⁴, 278, F₂, 6, 124) (dual of [(278, 6), 1414, 125]-NRT-code)	[i]
12	No linear OOA(2²⁵⁴, 278, F₂, 7, 124) (dual of [(278, 7), 1692, 125]-NRT-code)	[i]
13	No linear OOA(2²⁵⁴, 278, F₂, 8, 124) (dual of [(278, 8), 1970, 125]-NRT-code)	[i]
14	No digital (130, 254, 278)-net over F₂	[i]		Extracting Embedded Orthogonal Array
15	No linear OA(2²⁵⁵, 288, F₂, 124) (dual of [288, 33, 125]-code)	[i]		ConstructionÂ Y1 (Bound)