Information on Result #547571
There is no linear OA(818, 27, F8, 16) (dual of [27, 9, 17]-code), because residual code would yield OA(82, 10, S8, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 71 > 82 [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.
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(819, 28, F8, 17) (dual of [28, 9, 18]-code) | [i] | Truncation | |
| 2 | No linear OA(820, 29, F8, 18) (dual of [29, 9, 19]-code) | [i] | ||
| 3 | No linear OA(821, 30, F8, 19) (dual of [30, 9, 20]-code) | [i] | ||
| 4 | No linear OA(822, 31, F8, 20) (dual of [31, 9, 21]-code) | [i] | ||
| 5 | No linear OA(823, 32, F8, 21) (dual of [32, 9, 22]-code) | [i] | ||
| 6 | No linear OOA(819, 27, F8, 2, 17) (dual of [(27, 2), 35, 18]-NRT-code) | [i] | m-Reduction for OOAs | |
| 7 | No linear OOA(820, 27, F8, 2, 18) (dual of [(27, 2), 34, 19]-NRT-code) | [i] | ||
| 8 | No linear OOA(821, 27, F8, 2, 19) (dual of [(27, 2), 33, 20]-NRT-code) | [i] | ||
| 9 | No linear OOA(822, 27, F8, 2, 20) (dual of [(27, 2), 32, 21]-NRT-code) | [i] | ||
| 10 | No linear OOA(823, 27, F8, 2, 21) (dual of [(27, 2), 31, 22]-NRT-code) | [i] | ||
| 11 | No linear OOA(824, 27, F8, 2, 22) (dual of [(27, 2), 30, 23]-NRT-code) | [i] | ||
| 12 | No linear OOA(825, 27, F8, 2, 23) (dual of [(27, 2), 29, 24]-NRT-code) | [i] | ||
| 13 | No linear OOA(818, 27, F8, 2, 16) (dual of [(27, 2), 36, 17]-NRT-code) | [i] | Depth Reduction | |
| 14 | No linear OOA(818, 27, F8, 3, 16) (dual of [(27, 3), 63, 17]-NRT-code) | [i] | ||
| 15 | No digital (2, 18, 27)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 16 | No linear OA(8146, 156, F8, 128) (dual of [156, 10, 129]-code) | [i] | Residual Code | |
| 17 | No linear OA(816, 34, F8, 14) (dual of [34, 18, 15]-code) | [i] | Construction Y1 (Bound) | |
| 18 | No linear OA(814, 32, F8, 12) (dual of [32, 18, 13]-code) | [i] | ||