Information on Result #548644
There is no linear OA(814, 32, F8, 12) (dual of [32, 18, 13]-code), because construction Y1 would yield
- linear OA(813, 16, F8, 12) (dual of [16, 3, 13]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(818, 32, F8, 16) (dual of [32, 14, 17]-code), but
- discarding factors / shortening the dual code would yield linear OA(818, 27, F8, 16) (dual of [27, 9, 17]-code), but
- residual code [i] 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]
- residual code [i] would yield OA(82, 10, S8, 2), but
- discarding factors / shortening the dual code would yield linear OA(818, 27, F8, 16) (dual of [27, 9, 17]-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.
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(815, 33, F8, 13) (dual of [33, 18, 14]-code) | [i] | Truncation | |
| 2 | No linear OA(817, 35, F8, 15) (dual of [35, 18, 16]-code) | [i] | ||
| 3 | No linear OOA(815, 32, F8, 2, 13) (dual of [(32, 2), 49, 14]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(816, 32, F8, 2, 14) (dual of [(32, 2), 48, 15]-NRT-code) | [i] | ||
| 5 | No linear OOA(817, 32, F8, 2, 15) (dual of [(32, 2), 47, 16]-NRT-code) | [i] | ||
| 6 | No linear OOA(814, 32, F8, 2, 12) (dual of [(32, 2), 50, 13]-NRT-code) | [i] | Depth Reduction | |
| 7 | No linear OOA(814, 32, F8, 3, 12) (dual of [(32, 3), 82, 13]-NRT-code) | [i] | ||
| 8 | No digital (2, 14, 32)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 9 | No linear OA(832, 46, F8, 28) (dual of [46, 14, 29]-code) | [i] | Construction Y1 (Bound) | |