Information on Result #547969
There is no linear OA(714, 30, F7, 12) (dual of [30, 16, 13]-code), because construction Y1 would yield
- linear OA(713, 16, F7, 12) (dual of [16, 3, 13]-code), but
- linear OA(716, 30, F7, 14) (dual of [30, 14, 15]-code), but
- discarding factors / shortening the dual code would yield linear OA(716, 24, F7, 14) (dual of [24, 8, 15]-code), but
- residual code [i] would yield OA(72, 9, S7, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 55 > 72 [i]
- residual code [i] would yield OA(72, 9, S7, 2), but
- discarding factors / shortening the dual code would yield linear OA(716, 24, F7, 14) (dual of [24, 8, 15]-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(715, 31, F7, 13) (dual of [31, 16, 14]-code) | [i] | Truncation | |
| 2 | No linear OOA(715, 30, F7, 2, 13) (dual of [(30, 2), 45, 14]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(714, 30, F7, 2, 12) (dual of [(30, 2), 46, 13]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(714, 30, F7, 3, 12) (dual of [(30, 3), 76, 13]-NRT-code) | [i] | ||
| 5 | No digital (2, 14, 30)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(721, 35, F7, 18) (dual of [35, 14, 19]-code) | [i] | Construction Y1 (Bound) | |