Information on Result #548645
There is no linear OA(832, 46, F8, 28) (dual of [46, 14, 29]-code), because construction Y1 would yield
- linear OA(831, 34, F8, 28) (dual of [34, 3, 29]-code), but
- “Mas†bound on codes from Brouwer’s database [i]
- linear OA(814, 46, F8, 12) (dual of [46, 32, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(814, 32, F8, 12) (dual of [32, 18, 13]-code), but
- construction Y1 [i] 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
- linear OA(813, 16, F8, 12) (dual of [16, 3, 13]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(814, 32, F8, 12) (dual of [32, 18, 13]-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(833, 47, F8, 29) (dual of [47, 14, 30]-code) | [i] | Truncation | |
| 2 | No linear OA(834, 48, F8, 30) (dual of [48, 14, 31]-code) | [i] | ||
| 3 | No linear OA(835, 49, F8, 31) (dual of [49, 14, 32]-code) | [i] | ||
| 4 | No linear OOA(833, 46, F8, 2, 29) (dual of [(46, 2), 59, 30]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(834, 46, F8, 2, 30) (dual of [(46, 2), 58, 31]-NRT-code) | [i] | ||
| 6 | No linear OOA(835, 46, F8, 2, 31) (dual of [(46, 2), 57, 32]-NRT-code) | [i] | ||
| 7 | No linear OOA(832, 46, F8, 2, 28) (dual of [(46, 2), 60, 29]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(832, 46, F8, 3, 28) (dual of [(46, 3), 106, 29]-NRT-code) | [i] | ||
| 9 | No digital (4, 32, 46)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(831, 63, F8, 27) (dual of [63, 32, 28]-code) | [i] | Construction Y1 (Bound) | |