Information on Result #613606
Linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8
Mode: Constructive and 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(547, 78131, F5, 8) (dual of [78131, 78084, 9]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(548, 78136, F5, 8) (dual of [78136, 78088, 9]-code) | [i] | ||
| 3 | Linear OOA(543, 58469, F5, 2, 8) (dual of [(58469, 2), 116895, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(543, 58469, F5, 3, 8) (dual of [(58469, 3), 175364, 9]-NRT-code) | [i] | ||
| 5 | Digital (35, 43, 58469)-net over F5 | [i] | ||
| 6 | Linear OA(548, 78131, F5, 8) (dual of [78131, 78083, 9]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 7 | Linear OA(550, 78132, F5, 9) (dual of [78132, 78082, 10]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(543, 78132, F5, 8) (dual of [78132, 78089, 9]-code) | [i] | ✔ | |
| 9 | Linear OA(558, 78140, F5, 10) (dual of [78140, 78082, 11]-code) | [i] | ✔ | |
| 10 | Linear OA(560, 78142, F5, 11) (dual of [78142, 78082, 12]-code) | [i] | ✔ | |
| 11 | Linear OA(544, 78140, F5, 8) (dual of [78140, 78096, 9]-code) | [i] | ✔ | |
| 12 | Linear OA(568, 78150, F5, 12) (dual of [78150, 78082, 13]-code) | [i] | ✔ | |
| 13 | Linear OA(547, 78150, F5, 8) (dual of [78150, 78103, 9]-code) | [i] | ✔ | |
| 14 | Linear OA(579, 78161, F5, 13) (dual of [78161, 78082, 14]-code) | [i] | ✔ | |
| 15 | Linear OA(588, 78170, F5, 14) (dual of [78170, 78082, 15]-code) | [i] | ✔ | |
| 16 | Linear OA(577, 78155, F5, 13) (dual of [78155, 78078, 14]-code) | [i] | ✔ | |
| 17 | Linear OA(578, 78160, F5, 13) (dual of [78160, 78082, 14]-code) | [i] | ✔ | |
| 18 | Linear OA(587, 78169, F5, 14) (dual of [78169, 78082, 15]-code) | [i] | ✔ | |
| 19 | Linear OA(578, 78155, F5, 13) (dual of [78155, 78077, 14]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 20 | Linear OA(576, 78152, F5, 13) (dual of [78152, 78076, 14]-code) | [i] | ✔ | |
| 21 | Linear OA(571, 78155, F5, 12) (dual of [78155, 78084, 13]-code) | [i] | ✔ | |
| 22 | Linear OA(569, 78152, F5, 12) (dual of [78152, 78083, 13]-code) | [i] | ✔ | |
| 23 | Linear OA(559, 78135, F5, 11) (dual of [78135, 78076, 12]-code) | [i] | ✔ | |
| 24 | Linear OA(548, 78152, F5, 8) (dual of [78152, 78104, 9]-code) | [i] | ✔ | |
| 25 | Linear OA(558, 78141, F5, 10) (dual of [78141, 78083, 11]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 26 | Linear OA(544, 78141, F5, 8) (dual of [78141, 78097, 9]-code) | [i] | ✔ | |