Information on Result #548617
There is no linear OA(454, 67, F4, 40) (dual of [67, 13, 41]-code), because construction Y1 would yield
- linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- OA(413, 67, S4, 8), but
- the linear programming bound shows that M ≥ 921996 181504 / 13559 > 413 [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(455, 68, F4, 41) (dual of [68, 13, 42]-code) | [i] | Truncation | |
| 2 | No linear OOA(455, 67, F4, 2, 41) (dual of [(67, 2), 79, 42]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(454, 67, F4, 2, 40) (dual of [(67, 2), 80, 41]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(454, 67, F4, 3, 40) (dual of [(67, 3), 147, 41]-NRT-code) | [i] | ||
| 5 | No digital (14, 54, 67)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |