Information on Result #548692
There is no linear OA(725, 53, F7, 21) (dual of [53, 28, 22]-code), because construction Y1 would yield
- linear OA(724, 29, F7, 21) (dual of [29, 5, 22]-code), but
- construction Y1 [i] would yield
- OA(723, 25, S7, 21), but
- the (dual) Plotkin bound shows that M ≥ 383 162462 761132 828802 / 11 > 723 [i]
- OA(75, 29, S7, 4), but
- the linear programming bound shows that M ≥ 3 384381 / 197 > 75 [i]
- OA(723, 25, S7, 21), but
- construction Y1 [i] would yield
- linear OA(728, 53, F7, 24) (dual of [53, 25, 25]-code), but
- discarding factors / shortening the dual code would yield linear OA(728, 40, F7, 24) (dual of [40, 12, 25]-code), but
- construction Y1 [i] would yield
- linear OA(727, 30, F7, 24) (dual of [30, 3, 25]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(712, 40, F7, 10) (dual of [40, 28, 11]-code), but
- discarding factors / shortening the dual code would yield linear OA(712, 36, F7, 10) (dual of [36, 24, 11]-code), but
- construction Y1 [i] would yield
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-code), but
- “BPM†bound on codes from Brouwer’s database [i]
- linear OA(724, 36, F7, 21) (dual of [36, 12, 22]-code), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- residual code [i] would yield OA(73, 9, S7, 3), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(712, 36, F7, 10) (dual of [36, 24, 11]-code), but
- linear OA(727, 30, F7, 24) (dual of [30, 3, 25]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(728, 40, F7, 24) (dual of [40, 12, 25]-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(726, 54, F7, 22) (dual of [54, 28, 23]-code) | [i] | Truncation | |
| 2 | No linear OA(727, 55, F7, 23) (dual of [55, 28, 24]-code) | [i] | ||
| 3 | No linear OOA(726, 53, F7, 2, 22) (dual of [(53, 2), 80, 23]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(727, 53, F7, 2, 23) (dual of [(53, 2), 79, 24]-NRT-code) | [i] | ||
| 5 | No linear OOA(725, 53, F7, 2, 21) (dual of [(53, 2), 81, 22]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(725, 53, F7, 3, 21) (dual of [(53, 3), 134, 22]-NRT-code) | [i] | ||
| 7 | No digital (4, 25, 53)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |