MinT - Information on Result #551410

Information on Result #551410

There is no linear OOA(2¹¹⁰, 117, F₂, 2, 57) (dual of [(117, 2), 124, 58]-NRT-code), because 1 step m-reduction would yield linear OA(2¹⁰⁹, 117, F₂, 56) (dual of [117, 8, 57]-code), but

1 times code embedding in larger space [i] would yield linear OA(2¹¹⁰, 118, F₂, 56) (dual of [118, 8, 57]-code), but
- adding a parity check bit [i] would yield linear OA(2¹¹¹, 119, F₂, 57) (dual of [119, 8, 58]-code), but
  - â€œDMaâ€ 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(2¹¹⁰, 117, F₂, 3, 57) (dual of [(117, 3), 241, 58]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹¹⁰, 117, F₂, 4, 57) (dual of [(117, 4), 358, 58]-NRT-code)	[i]
3	No linear OOA(2¹¹⁰, 117, F₂, 5, 57) (dual of [(117, 5), 475, 58]-NRT-code)	[i]
4	No linear OOA(2¹¹⁰, 117, F₂, 6, 57) (dual of [(117, 6), 592, 58]-NRT-code)	[i]
5	No linear OOA(2¹¹⁰, 117, F₂, 7, 57) (dual of [(117, 7), 709, 58]-NRT-code)	[i]
6	No linear OOA(2¹¹⁰, 117, F₂, 8, 57) (dual of [(117, 8), 826, 58]-NRT-code)	[i]