MinT - Information on Result #548562

Information on Result #548562

There is no linear OA(2¹⁹⁵, 232, F₂, 92) (dual of [232, 37, 93]-code), because constructionÂ Y1 would yield

linear OA(2¹⁹⁴, 220, F₂, 92) (dual of [220, 26, 93]-code), but
- adding a parity check bit [i] would yield linear OA(2¹⁹⁵, 221, F₂, 93) (dual of [221, 26, 94]-code), but
  - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
OA(2³⁷, 232, S₂, 12), but
- discarding factors would yield OA(2³⁷, 217, S₂, 12), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 139173 045698 > 2³⁷ [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		This result only	Method
1	No linear OA(2¹⁹⁶, 233, F₂, 93) (dual of [233, 37, 94]-code)	[i]		Truncation
2	No linear OA(2¹⁹⁷, 234, F₂, 94) (dual of [234, 37, 95]-code)	[i]
3	No linear OA(2¹⁹⁸, 235, F₂, 95) (dual of [235, 37, 96]-code)	[i]
4	No linear OOA(2¹⁹⁶, 232, F₂, 2, 93) (dual of [(232, 2), 268, 94]-NRT-code)	[i]		m-Reduction for OOAs
5	No linear OOA(2¹⁹⁷, 232, F₂, 2, 94) (dual of [(232, 2), 267, 95]-NRT-code)	[i]
6	No linear OOA(2¹⁹⁸, 232, F₂, 2, 95) (dual of [(232, 2), 266, 96]-NRT-code)	[i]
7	No linear OOA(2¹⁹⁵, 232, F₂, 2, 92) (dual of [(232, 2), 269, 93]-NRT-code)	[i]		Depth Reduction
8	No linear OOA(2¹⁹⁵, 232, F₂, 3, 92) (dual of [(232, 3), 501, 93]-NRT-code)	[i]
9	No linear OOA(2¹⁹⁵, 232, F₂, 4, 92) (dual of [(232, 4), 733, 93]-NRT-code)	[i]
10	No linear OOA(2¹⁹⁵, 232, F₂, 5, 92) (dual of [(232, 5), 965, 93]-NRT-code)	[i]
11	No linear OOA(2¹⁹⁵, 232, F₂, 6, 92) (dual of [(232, 6), 1197, 93]-NRT-code)	[i]
12	No linear OOA(2¹⁹⁵, 232, F₂, 7, 92) (dual of [(232, 7), 1429, 93]-NRT-code)	[i]
13	No linear OOA(2¹⁹⁵, 232, F₂, 8, 92) (dual of [(232, 8), 1661, 93]-NRT-code)	[i]
14	No digital (103, 195, 232)-net over F₂	[i]		Extracting Embedded Orthogonal Array
15	No linear OA(2¹⁹⁶, 252, F₂, 92) (dual of [252, 56, 93]-code)	[i]		ConstructionÂ Y1 (Bound)