MinT - Information on Result #551770

Information on Result #551770

There is no linear OOA(2¹³², 165, F₂, 2, 63) (dual of [(165, 2), 198, 64]-NRT-code), because 1 step m-reduction would yield linear OA(2¹³¹, 165, F₂, 62) (dual of [165, 34, 63]-code), but

constructionÂ Y1 [i] would yield
1. 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]
2. 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(2¹³², 165, F₂, 3, 63) (dual of [(165, 3), 363, 64]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹³², 165, F₂, 4, 63) (dual of [(165, 4), 528, 64]-NRT-code)	[i]
3	No linear OOA(2¹³², 165, F₂, 5, 63) (dual of [(165, 5), 693, 64]-NRT-code)	[i]
4	No linear OOA(2¹³², 165, F₂, 6, 63) (dual of [(165, 6), 858, 64]-NRT-code)	[i]
5	No linear OOA(2¹³², 165, F₂, 7, 63) (dual of [(165, 7), 1023, 64]-NRT-code)	[i]
6	No linear OOA(2¹³², 165, F₂, 8, 63) (dual of [(165, 8), 1188, 64]-NRT-code)	[i]