MinT - Information on Result #548536

Information on Result #548536

There is no linear OA(2⁶⁵, 76, F₂, 32) (dual of [76, 11, 33]-code), because constructionÂ Y1 would yield

linear OA(2⁶⁴, 72, F₂, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(2⁶⁵, 73, F₂, 33) (dual of [73, 8, 34]-code), but
  - â€œBJVâ€ bound on codes from Brouwerâ€™s database [i]
OA(2¹¹, 76, S₂, 4), but
- discarding factors would yield OA(2¹¹, 64, S₂, 4), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2081 > 2¹¹ [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(2⁶⁶, 77, F₂, 33) (dual of [77, 11, 34]-code)	[i]		Truncation
2	No linear OOA(2⁶⁶, 76, F₂, 2, 33) (dual of [(76, 2), 86, 34]-NRT-code)	[i]		m-Reduction for OOAs
3	No linear OOA(2⁶⁵, 76, F₂, 2, 32) (dual of [(76, 2), 87, 33]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(2⁶⁵, 76, F₂, 3, 32) (dual of [(76, 3), 163, 33]-NRT-code)	[i]
5	No linear OOA(2⁶⁵, 76, F₂, 4, 32) (dual of [(76, 4), 239, 33]-NRT-code)	[i]
6	No linear OOA(2⁶⁵, 76, F₂, 5, 32) (dual of [(76, 5), 315, 33]-NRT-code)	[i]
7	No linear OOA(2⁶⁵, 76, F₂, 6, 32) (dual of [(76, 6), 391, 33]-NRT-code)	[i]
8	No linear OOA(2⁶⁵, 76, F₂, 7, 32) (dual of [(76, 7), 467, 33]-NRT-code)	[i]
9	No linear OOA(2⁶⁵, 76, F₂, 8, 32) (dual of [(76, 8), 543, 33]-NRT-code)	[i]
10	No digital (33, 65, 76)-net over F₂	[i]		Extracting Embedded Orthogonal Array
11	No linear OA(2⁶⁶, 82, F₂, 32) (dual of [82, 16, 33]-code)	[i]		ConstructionÂ Y1 (Bound)