Information on Result #548630
There is no linear OA(513, 37, F5, 10) (dual of [37, 24, 11]-code), because construction Y1 would yield
- linear OA(512, 17, F5, 10) (dual of [17, 5, 11]-code), but
- construction Y1 [i] would yield
- OA(511, 13, S5, 10), but
- the (dual) Plotkin bound shows that M ≥ 732 421875 / 11 > 511 [i]
- linear OA(55, 17, F5, 4) (dual of [17, 12, 5]-code), but
- discarding factors / shortening the dual code would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- OA(511, 13, S5, 10), but
- construction Y1 [i] would yield
- OA(524, 37, S5, 20), but
- discarding factors would yield OA(524, 34, S5, 20), but
- the linear programming bound shows that M ≥ 3333 389759 063720 703125 / 50344 > 524 [i]
- discarding factors would yield OA(524, 34, S5, 20), 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 OOA(513, 37, F5, 2, 10) (dual of [(37, 2), 61, 11]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(513, 37, F5, 3, 10) (dual of [(37, 3), 98, 11]-NRT-code) | [i] | ||
| 3 | No digital (3, 13, 37)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |