Information on Result #550827
There is no linear OOA(266, 76, F2, 2, 33) (dual of [(76, 2), 86, 34]-NRT-code), because 1 step m-reduction would yield linear OA(265, 76, F2, 32) (dual of [76, 11, 33]-code), but
- construction Y1 [i] would yield
- linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- OA(211, 76, S2, 4), but
- discarding factors would yield OA(211, 64, S2, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 2081 > 211 [i]
- discarding factors would yield OA(211, 64, S2, 4), but
- linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
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 | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(266, 76, F2, 3, 33) (dual of [(76, 3), 162, 34]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(266, 76, F2, 4, 33) (dual of [(76, 4), 238, 34]-NRT-code) | [i] | ||
| 3 | No linear OOA(266, 76, F2, 5, 33) (dual of [(76, 5), 314, 34]-NRT-code) | [i] | ||
| 4 | No linear OOA(266, 76, F2, 6, 33) (dual of [(76, 6), 390, 34]-NRT-code) | [i] | ||
| 5 | No linear OOA(266, 76, F2, 7, 33) (dual of [(76, 7), 466, 34]-NRT-code) | [i] | ||
| 6 | No linear OOA(266, 76, F2, 8, 33) (dual of [(76, 8), 542, 34]-NRT-code) | [i] | ||