Information on Result #559072
There is no linear OOA(417, 29, F4, 2, 13) (dual of [(29, 2), 41, 14]-NRT-code), because 1 step m-reduction would yield linear OA(416, 29, F4, 12) (dual of [29, 13, 13]-code), but
- construction Y1 [i] would yield
- linear OA(415, 19, F4, 12) (dual of [19, 4, 13]-code), but
- construction Y1 [i] would yield
- OA(414, 16, S4, 12), but
- the (dual) Plotkin bound shows that M ≥ 4294 967296 / 13 > 414 [i]
- linear OA(44, 19, F4, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,4)), but
- discarding factors / shortening the dual code would yield linear OA(44, 18, F4, 3) (dual of [18, 14, 4]-code or 18-cap in PG(3,4)), but
- OA(414, 16, S4, 12), but
- construction Y1 [i] would yield
- linear OA(413, 29, F4, 10) (dual of [29, 16, 11]-code), but
- discarding factors / shortening the dual code would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- linear OA(415, 19, F4, 12) (dual of [19, 4, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(417, 29, F4, 3, 13) (dual of [(29, 3), 70, 14]-NRT-code) | [i] | Depth Reduction | |