MinT - Information on Result #2174813

Information on Result #2174813

There is no linear OA(2¹⁹³, 219, F₂, 92) (dual of [219, 26, 93]-code), because 1 times code embedding in larger space 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]

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(2¹⁹⁴, 219, F₂, 2, 93) (dual of [(219, 2), 244, 94]-NRT-code)	[i]	m-Reduction for OOAs
2	No linear OOA(2¹⁹⁵, 219, F₂, 2, 94) (dual of [(219, 2), 243, 95]-NRT-code)	[i]
3	No linear OOA(2¹⁹⁶, 219, F₂, 2, 95) (dual of [(219, 2), 242, 96]-NRT-code)	[i]
4	No linear OOA(2¹⁹⁷, 219, F₂, 2, 96) (dual of [(219, 2), 241, 97]-NRT-code)	[i]
5	No linear OOA(2¹⁹⁸, 219, F₂, 2, 97) (dual of [(219, 2), 240, 98]-NRT-code)	[i]
6	No linear OOA(2¹⁹⁹, 219, F₂, 2, 98) (dual of [(219, 2), 239, 99]-NRT-code)	[i]
7	No linear OOA(2²⁰⁰, 219, F₂, 2, 99) (dual of [(219, 2), 238, 100]-NRT-code)	[i]
8	No linear OOA(2¹⁹³, 219, F₂, 2, 92) (dual of [(219, 2), 245, 93]-NRT-code)	[i]	Depth Reduction
9	No linear OOA(2¹⁹³, 219, F₂, 3, 92) (dual of [(219, 3), 464, 93]-NRT-code)	[i]
10	No linear OOA(2¹⁹³, 219, F₂, 4, 92) (dual of [(219, 4), 683, 93]-NRT-code)	[i]
11	No linear OOA(2¹⁹³, 219, F₂, 5, 92) (dual of [(219, 5), 902, 93]-NRT-code)	[i]
12	No linear OOA(2¹⁹³, 219, F₂, 6, 92) (dual of [(219, 6), 1121, 93]-NRT-code)	[i]
13	No linear OOA(2¹⁹³, 219, F₂, 7, 92) (dual of [(219, 7), 1340, 93]-NRT-code)	[i]
14	No linear OOA(2¹⁹³, 219, F₂, 8, 92) (dual of [(219, 8), 1559, 93]-NRT-code)	[i]
15	No digital (101, 193, 219)-net over F₂	[i]	Extracting Embedded Orthogonal Array