MinT - Information on Result #554269

Information on Result #554269

There is no linear OOA(2²²⁵, 215, F₂, 2, 123) (dual of [(215, 2), 205, 124]-NRT-code), because 19 step m-reduction would yield linear OA(2²⁰⁶, 215, F₂, 104) (dual of [215, 9, 105]-code), but

residual code [i] would yield linear OA(2¹⁰², 110, F₂, 52) (dual of [110, 8, 53]-code), but
- residual code [i] would yield linear OA(2⁵⁰, 57, F₂, 26) (dual of [57, 7, 27]-code), but
  - adding a parity check bit [i] would yield linear OA(2⁵¹, 58, F₂, 27) (dual of [58, 7, 28]-code), but
    - â€œvT3â€ 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(2²²⁵, 215, F₂, 3, 123) (dual of [(215, 3), 420, 124]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2²²⁵, 215, F₂, 4, 123) (dual of [(215, 4), 635, 124]-NRT-code)	[i]
3	No linear OOA(2²²⁵, 215, F₂, 5, 123) (dual of [(215, 5), 850, 124]-NRT-code)	[i]
4	No linear OOA(2²²⁵, 215, F₂, 6, 123) (dual of [(215, 6), 1065, 124]-NRT-code)	[i]
5	No linear OOA(2²²⁵, 215, F₂, 7, 123) (dual of [(215, 7), 1280, 124]-NRT-code)	[i]
6	No linear OOA(2²²⁵, 215, F₂, 8, 123) (dual of [(215, 8), 1495, 124]-NRT-code)	[i]