Information on Result #547883
There is no linear OA(4155, 170, F4, 116) (dual of [170, 15, 117]-code), because construction Y1 would yield
- linear OA(4154, 162, F4, 116) (dual of [162, 8, 117]-code), but
- construction Y1 [i] would yield
- linear OA(4153, 158, F4, 116) (dual of [158, 5, 117]-code), but
- residual code [i] would yield linear OA(437, 41, F4, 29) (dual of [41, 4, 30]-code), but
- 1 times truncation [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- 1 times truncation [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(437, 41, F4, 29) (dual of [41, 4, 30]-code), but
- OA(48, 162, S4, 4), but
- discarding factors would yield OA(48, 121, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 65704 > 48 [i]
- discarding factors would yield OA(48, 121, S4, 4), but
- linear OA(4153, 158, F4, 116) (dual of [158, 5, 117]-code), but
- construction Y1 [i] would yield
- OA(415, 170, S4, 8), but
- discarding factors would yield OA(415, 135, S4, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1082 768311 > 415 [i]
- discarding factors would yield OA(415, 135, S4, 8), 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(4156, 171, F4, 117) (dual of [171, 15, 118]-code) | [i] | Truncation | |
| 2 | No linear OA(4157, 172, F4, 118) (dual of [172, 15, 119]-code) | [i] | ||
| 3 | No linear OA(4158, 173, F4, 119) (dual of [173, 15, 120]-code) | [i] | ||
| 4 | No linear OOA(4156, 170, F4, 2, 117) (dual of [(170, 2), 184, 118]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4157, 170, F4, 2, 118) (dual of [(170, 2), 183, 119]-NRT-code) | [i] | ||
| 6 | No linear OOA(4158, 170, F4, 2, 119) (dual of [(170, 2), 182, 120]-NRT-code) | [i] | ||
| 7 | No linear OOA(4155, 170, F4, 2, 116) (dual of [(170, 2), 185, 117]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4155, 170, F4, 3, 116) (dual of [(170, 3), 355, 117]-NRT-code) | [i] | ||
| 9 | No digital (39, 155, 170)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(4156, 190, F4, 116) (dual of [190, 34, 117]-code) | [i] | Construction Y1 (Bound) | |