Information on Result #548625
There is no linear OA(4235, 247, F4, 176) (dual of [247, 12, 177]-code), because construction Y1 would yield
- linear OA(4234, 241, F4, 176) (dual of [241, 7, 177]-code), but
- residual code [i] would yield linear OA(458, 64, F4, 44) (dual of [64, 6, 45]-code), but
- residual code [i] would yield linear OA(414, 19, F4, 11) (dual of [19, 5, 12]-code), but
- 1 times truncation [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- 1 times truncation [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- residual code [i] would yield linear OA(414, 19, F4, 11) (dual of [19, 5, 12]-code), but
- residual code [i] would yield linear OA(458, 64, F4, 44) (dual of [64, 6, 45]-code), but
- OA(412, 247, S4, 6), but
- discarding factors would yield OA(412, 156, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 16 866019 > 412 [i]
- discarding factors would yield OA(412, 156, S4, 6), 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(4236, 248, F4, 177) (dual of [248, 12, 178]-code) | [i] | Truncation | |
| 2 | No linear OA(4237, 249, F4, 178) (dual of [249, 12, 179]-code) | [i] | ||
| 3 | No linear OA(4238, 250, F4, 179) (dual of [250, 12, 180]-code) | [i] | ||
| 4 | No linear OOA(4236, 247, F4, 2, 177) (dual of [(247, 2), 258, 178]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4237, 247, F4, 2, 178) (dual of [(247, 2), 257, 179]-NRT-code) | [i] | ||
| 6 | No linear OOA(4238, 247, F4, 2, 179) (dual of [(247, 2), 256, 180]-NRT-code) | [i] | ||
| 7 | No linear OOA(4235, 247, F4, 2, 176) (dual of [(247, 2), 259, 177]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4235, 247, F4, 3, 176) (dual of [(247, 3), 506, 177]-NRT-code) | [i] | ||
| 9 | No digital (59, 235, 247)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |