MinT - Information on Result #554767

Information on Result #554767

There is no linear OOA(2²⁴⁵, 250, F₂, 2, 126) (dual of [(250, 2), 255, 127]-NRT-code), because 6 step m-reduction would yield linear OA(2²³⁹, 250, F₂, 120) (dual of [250, 11, 121]-code), but

residual code [i] would yield linear OA(2¹¹⁹, 129, F₂, 60) (dual of [129, 10, 61]-code), but
- residual code [i] would yield linear OA(2⁵⁹, 68, F₂, 30) (dual of [68, 9, 31]-code), but
  - adding a parity check bit [i] would yield linear OA(2⁶⁰, 69, F₂, 31) (dual of [69, 9, 32]-code), but
    - â€œBGVâ€ 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(2²⁴⁵, 250, F₂, 3, 126) (dual of [(250, 3), 505, 127]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2²⁴⁵, 250, F₂, 4, 126) (dual of [(250, 4), 755, 127]-NRT-code)	[i]
3	No linear OOA(2²⁴⁵, 250, F₂, 5, 126) (dual of [(250, 5), 1005, 127]-NRT-code)	[i]
4	No linear OOA(2²⁴⁵, 250, F₂, 6, 126) (dual of [(250, 6), 1255, 127]-NRT-code)	[i]
5	No linear OOA(2²⁴⁵, 250, F₂, 7, 126) (dual of [(250, 7), 1505, 127]-NRT-code)	[i]
6	No linear OOA(2²⁴⁵, 250, F₂, 8, 126) (dual of [(250, 8), 1755, 127]-NRT-code)	[i]