MinT - Information on Result #555152

Information on Result #555152

There is no linear OOA(2²⁵⁷, 248, F₂, 2, 139) (dual of [(248, 2), 239, 140]-NRT-code), because 19 step m-reduction would yield linear OA(2²³⁸, 248, F₂, 120) (dual of [248, 10, 121]-code), but

residual code [i] would yield linear OA(2¹¹⁸, 127, F₂, 60) (dual of [127, 9, 61]-code), but
- residual code [i] would yield linear OA(2⁵⁸, 66, F₂, 30) (dual of [66, 8, 31]-code), but
  - adding a parity check bit [i] would yield linear OA(2⁵⁹, 67, F₂, 31) (dual of [67, 8, 32]-code), but
    - â€œDHMâ€ 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(2²⁵⁷, 248, F₂, 3, 139) (dual of [(248, 3), 487, 140]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2²⁵⁷, 248, F₂, 4, 139) (dual of [(248, 4), 735, 140]-NRT-code)	[i]
3	No linear OOA(2²⁵⁷, 248, F₂, 5, 139) (dual of [(248, 5), 983, 140]-NRT-code)	[i]
4	No linear OOA(2²⁵⁷, 248, F₂, 6, 139) (dual of [(248, 6), 1231, 140]-NRT-code)	[i]
5	No linear OOA(2²⁵⁷, 248, F₂, 7, 139) (dual of [(248, 7), 1479, 140]-NRT-code)	[i]
6	No linear OOA(2²⁵⁷, 248, F₂, 8, 139) (dual of [(248, 8), 1727, 140]-NRT-code)	[i]