Information on Result #548507
There is no linear OA(4234, 241, F4, 176) (dual of [241, 7, 177]-code), because residual code 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
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(4235, 242, F4, 177) (dual of [242, 7, 178]-code) | [i] | Truncation | |
| 2 | No linear OA(4236, 243, F4, 178) (dual of [243, 7, 179]-code) | [i] | ||
| 3 | No linear OA(4237, 244, F4, 179) (dual of [244, 7, 180]-code) | [i] | ||
| 4 | No linear OOA(4235, 241, F4, 2, 177) (dual of [(241, 2), 247, 178]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4236, 241, F4, 2, 178) (dual of [(241, 2), 246, 179]-NRT-code) | [i] | ||
| 6 | No linear OOA(4237, 241, F4, 2, 179) (dual of [(241, 2), 245, 180]-NRT-code) | [i] | ||
| 7 | No linear OOA(4238, 241, F4, 2, 180) (dual of [(241, 2), 244, 181]-NRT-code) | [i] | ||
| 8 | No linear OOA(4239, 241, F4, 2, 181) (dual of [(241, 2), 243, 182]-NRT-code) | [i] | ||
| 9 | No linear OOA(4240, 241, F4, 2, 182) (dual of [(241, 2), 242, 183]-NRT-code) | [i] | ||
| 10 | No linear OOA(4241, 241, F4, 2, 183) (dual of [(241, 2), 241, 184]-NRT-code) | [i] | ||
| 11 | No linear OOA(4242, 241, F4, 2, 184) (dual of [(241, 2), 240, 185]-NRT-code) | [i] | ||
| 12 | No linear OOA(4243, 241, F4, 2, 185) (dual of [(241, 2), 239, 186]-NRT-code) | [i] | ||
| 13 | No linear OOA(4244, 241, F4, 2, 186) (dual of [(241, 2), 238, 187]-NRT-code) | [i] | ||
| 14 | No linear OOA(4245, 241, F4, 2, 187) (dual of [(241, 2), 237, 188]-NRT-code) | [i] | ||
| 15 | No linear OOA(4246, 241, F4, 2, 188) (dual of [(241, 2), 236, 189]-NRT-code) | [i] | ||
| 16 | No linear OOA(4247, 241, F4, 2, 189) (dual of [(241, 2), 235, 190]-NRT-code) | [i] | ||
| 17 | No linear OOA(4248, 241, F4, 2, 190) (dual of [(241, 2), 234, 191]-NRT-code) | [i] | ||
| 18 | No linear OOA(4249, 241, F4, 2, 191) (dual of [(241, 2), 233, 192]-NRT-code) | [i] | ||
| 19 | No linear OOA(4250, 241, F4, 2, 192) (dual of [(241, 2), 232, 193]-NRT-code) | [i] | ||
| 20 | No linear OOA(4251, 241, F4, 2, 193) (dual of [(241, 2), 231, 194]-NRT-code) | [i] | ||
| 21 | No linear OOA(4252, 241, F4, 2, 194) (dual of [(241, 2), 230, 195]-NRT-code) | [i] | ||
| 22 | No linear OOA(4253, 241, F4, 2, 195) (dual of [(241, 2), 229, 196]-NRT-code) | [i] | ||
| 23 | No linear OOA(4254, 241, F4, 2, 196) (dual of [(241, 2), 228, 197]-NRT-code) | [i] | ||
| 24 | No linear OOA(4255, 241, F4, 2, 197) (dual of [(241, 2), 227, 198]-NRT-code) | [i] | ||
| 25 | No linear OOA(4256, 241, F4, 2, 198) (dual of [(241, 2), 226, 199]-NRT-code) | [i] | ||
| 26 | No linear OOA(4257, 241, F4, 2, 199) (dual of [(241, 2), 225, 200]-NRT-code) | [i] | ||
| 27 | No linear OOA(4258, 241, F4, 2, 200) (dual of [(241, 2), 224, 201]-NRT-code) | [i] | ||
| 28 | No linear OOA(4259, 241, F4, 2, 201) (dual of [(241, 2), 223, 202]-NRT-code) | [i] | ||
| 29 | No linear OOA(4260, 241, F4, 2, 202) (dual of [(241, 2), 222, 203]-NRT-code) | [i] | ||
| 30 | No linear OOA(4234, 241, F4, 2, 176) (dual of [(241, 2), 248, 177]-NRT-code) | [i] | Depth Reduction | |
| 31 | No linear OOA(4234, 241, F4, 3, 176) (dual of [(241, 3), 489, 177]-NRT-code) | [i] | ||
| 32 | No digital (58, 234, 241)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 33 | No linear OA(4235, 247, F4, 176) (dual of [247, 12, 177]-code) | [i] | Construction Y1 (Bound) | |