MinT - Information on Result #551508

Information on Result #551508

There is no linear OOA(2¹¹⁶, 112, F₂, 2, 65) (dual of [(112, 2), 108, 66]-NRT-code), because 13 step m-reduction would yield linear OA(2¹⁰³, 112, F₂, 52) (dual of [112, 9, 53]-code), but

residual code [i] would yield linear OA(2⁵¹, 59, F₂, 26) (dual of [59, 8, 27]-code), but
- adding a parity check bit [i] would yield linear OA(2⁵², 60, F₂, 27) (dual of [60, 8, 28]-code), but
  - â€œBJVâ€ 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(2¹¹⁶, 112, F₂, 3, 65) (dual of [(112, 3), 220, 66]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹¹⁶, 112, F₂, 4, 65) (dual of [(112, 4), 332, 66]-NRT-code)	[i]
3	No linear OOA(2¹¹⁶, 112, F₂, 5, 65) (dual of [(112, 5), 444, 66]-NRT-code)	[i]
4	No linear OOA(2¹¹⁶, 112, F₂, 6, 65) (dual of [(112, 6), 556, 66]-NRT-code)	[i]
5	No linear OOA(2¹¹⁶, 112, F₂, 7, 65) (dual of [(112, 7), 668, 66]-NRT-code)	[i]
6	No linear OOA(2¹¹⁶, 112, F₂, 8, 65) (dual of [(112, 8), 780, 66]-NRT-code)	[i]