MinT - Information on Result #548540

Information on Result #548540

There is no linear OA(2¹³¹, 165, F₂, 62) (dual of [165, 34, 63]-code), because constructionÂ Y1 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]
OA(2³⁴, 165, S₂, 12), but
- discarding factors would yield OA(2³⁴, 154, S₂, 12), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17486 314616 > 2³⁴ [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(2¹³², 166, F₂, 63) (dual of [166, 34, 64]-code)	[i]		Truncation
2	No linear OOA(2¹³², 165, F₂, 2, 63) (dual of [(165, 2), 198, 64]-NRT-code)	[i]		m-Reduction for OOAs
3	No linear OOA(2¹³¹, 165, F₂, 2, 62) (dual of [(165, 2), 199, 63]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(2¹³¹, 165, F₂, 3, 62) (dual of [(165, 3), 364, 63]-NRT-code)	[i]
5	No linear OOA(2¹³¹, 165, F₂, 4, 62) (dual of [(165, 4), 529, 63]-NRT-code)	[i]
6	No linear OOA(2¹³¹, 165, F₂, 5, 62) (dual of [(165, 5), 694, 63]-NRT-code)	[i]
7	No linear OOA(2¹³¹, 165, F₂, 6, 62) (dual of [(165, 6), 859, 63]-NRT-code)	[i]
8	No linear OOA(2¹³¹, 165, F₂, 7, 62) (dual of [(165, 7), 1024, 63]-NRT-code)	[i]
9	No linear OOA(2¹³¹, 165, F₂, 8, 62) (dual of [(165, 8), 1189, 63]-NRT-code)	[i]
10	No digital (69, 131, 165)-net over F₂	[i]		Extracting Embedded Orthogonal Array
11	No linear OA(2¹³², 185, F₂, 62) (dual of [185, 53, 63]-code)	[i]		ConstructionÂ Y1 (Bound)