MinT - Information on Result #548548

Information on Result #548548

There is no linear OA(2¹⁶⁵, 219, F₂, 76) (dual of [219, 54, 77]-code), because constructionÂ Y1 would yield

linear OA(2¹⁶⁴, 199, F₂, 76) (dual of [199, 35, 77]-code), but
- adding a parity check bit [i] would yield linear OA(2¹⁶⁵, 200, F₂, 77) (dual of [200, 35, 78]-code), but
  - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
OA(2⁵⁴, 219, S₂, 20), but
- discarding factors would yield OA(2⁵⁴, 195, S₂, 20), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18304 094847 646336 > 2⁵⁴ [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(2¹⁶⁶, 220, F₂, 77) (dual of [220, 54, 78]-code)	[i]		Truncation
2	No linear OOA(2¹⁶⁶, 219, F₂, 2, 77) (dual of [(219, 2), 272, 78]-NRT-code)	[i]		m-Reduction for OOAs
3	No linear OOA(2¹⁶⁵, 219, F₂, 2, 76) (dual of [(219, 2), 273, 77]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(2¹⁶⁵, 219, F₂, 3, 76) (dual of [(219, 3), 492, 77]-NRT-code)	[i]
5	No linear OOA(2¹⁶⁵, 219, F₂, 4, 76) (dual of [(219, 4), 711, 77]-NRT-code)	[i]
6	No linear OOA(2¹⁶⁵, 219, F₂, 5, 76) (dual of [(219, 5), 930, 77]-NRT-code)	[i]
7	No linear OOA(2¹⁶⁵, 219, F₂, 6, 76) (dual of [(219, 6), 1149, 77]-NRT-code)	[i]
8	No linear OOA(2¹⁶⁵, 219, F₂, 7, 76) (dual of [(219, 7), 1368, 77]-NRT-code)	[i]
9	No linear OOA(2¹⁶⁵, 219, F₂, 8, 76) (dual of [(219, 8), 1587, 77]-NRT-code)	[i]
10	No digital (89, 165, 219)-net over F₂	[i]		Extracting Embedded Orthogonal Array
11	No linear OA(2¹⁶⁶, 253, F₂, 76) (dual of [253, 87, 77]-code)	[i]		ConstructionÂ Y1 (Bound)