Information on Result #613598
Linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7
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(539, 78131, F5, 7) (dual of [78131, 78092, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(540, 78151, F5, 7) (dual of [78151, 78111, 8]-code) | [i] | ||
| 3 | Linear OOA(536, 50879, F5, 2, 7) (dual of [(50879, 2), 101722, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(536, 50879, F5, 3, 7) (dual of [(50879, 3), 152601, 8]-NRT-code) | [i] | ||
| 5 | Digital (29, 36, 50879)-net over F5 | [i] | ||
| 6 | Linear OA(543, 78132, F5, 8) (dual of [78132, 78089, 9]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 7 | Linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code) | [i] | ✔ | |
| 8 | Linear OA(551, 78140, F5, 9) (dual of [78140, 78089, 10]-code) | [i] | ✔ | |
| 9 | Linear OA(539, 78142, F5, 7) (dual of [78142, 78103, 8]-code) | [i] | ✔ | |
| 10 | Linear OA(561, 78150, F5, 11) (dual of [78150, 78089, 12]-code) | [i] | ✔ | |
| 11 | Linear OA(572, 78161, F5, 12) (dual of [78161, 78089, 13]-code) | [i] | ✔ | |
| 12 | Linear OA(570, 78155, F5, 12) (dual of [78155, 78085, 13]-code) | [i] | ✔ | |
| 13 | Linear OA(571, 78160, F5, 12) (dual of [78160, 78089, 13]-code) | [i] | ✔ | |
| 14 | Linear OA(580, 78169, F5, 13) (dual of [78169, 78089, 14]-code) | [i] | ✔ | |
| 15 | Linear OA(571, 78155, F5, 12) (dual of [78155, 78084, 13]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 16 | Linear OA(569, 78152, F5, 12) (dual of [78152, 78083, 13]-code) | [i] | ✔ | |
| 17 | Linear OA(564, 78155, F5, 11) (dual of [78155, 78091, 12]-code) | [i] | ✔ | |
| 18 | Linear OA(562, 78152, F5, 11) (dual of [78152, 78090, 12]-code) | [i] | ✔ | |
| 19 | Linear OA(537, 78134, F5, 7) (dual of [78134, 78097, 8]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 20 | Linear OA(551, 78141, F5, 9) (dual of [78141, 78090, 10]-code) | [i] | ✔ | |