Information on Result #548537
There is no linear OA(266, 82, F2, 32) (dual of [82, 16, 33]-code), because construction Y1 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
- construction Y1 [i] would yield
- OA(216, 82, S2, 6), but
- discarding factors would yield OA(216, 74, S2, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 67600 > 216 [i]
- discarding factors would yield OA(216, 74, S2, 6), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(267, 83, F2, 33) (dual of [83, 16, 34]-code) | [i] | Truncation | |
| 2 | No linear OOA(267, 82, F2, 2, 33) (dual of [(82, 2), 97, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(266, 82, F2, 2, 32) (dual of [(82, 2), 98, 33]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(266, 82, F2, 3, 32) (dual of [(82, 3), 180, 33]-NRT-code) | [i] | ||
| 5 | No linear OOA(266, 82, F2, 4, 32) (dual of [(82, 4), 262, 33]-NRT-code) | [i] | ||
| 6 | No linear OOA(266, 82, F2, 5, 32) (dual of [(82, 5), 344, 33]-NRT-code) | [i] | ||
| 7 | No linear OOA(266, 82, F2, 6, 32) (dual of [(82, 6), 426, 33]-NRT-code) | [i] | ||
| 8 | No linear OOA(266, 82, F2, 7, 32) (dual of [(82, 7), 508, 33]-NRT-code) | [i] | ||
| 9 | No linear OOA(266, 82, F2, 8, 32) (dual of [(82, 8), 590, 33]-NRT-code) | [i] | ||
| 10 | No digital (34, 66, 82)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |