Information on Result #682381
Linear OA(599, 78126, F5, 17) (dual of [78126, 78027, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound)
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 OOA(599, 59188, F5, 2, 17) (dual of [(59188, 2), 118277, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(599, 59188, F5, 3, 17) (dual of [(59188, 3), 177465, 18]-NRT-code) | [i] | ||
| 3 | Digital (82, 99, 59188)-net over F5 | [i] | ||
| 4 | Linear OA(5114, 78141, F5, 19) (dual of [78141, 78027, 20]-code) | [i] | ✔ | Construction X with Cyclic Codes |
| 5 | Linear OA(5116, 78132, F5, 21) (dual of [78132, 78016, 22]-code) | [i] | ✔ | |
| 6 | Linear OA(5117, 78144, F5, 21) (dual of [78144, 78027, 22]-code) | [i] | ✔ | |
| 7 | Linear OA(5115, 78132, F5, 20) (dual of [78132, 78017, 21]-code) | [i] | ✔ | |
| 8 | Linear OA(5100, 78141, F5, 17) (dual of [78141, 78041, 18]-code) | [i] | ✔ | |
| 9 | Linear OA(5135, 78150, F5, 23) (dual of [78150, 78015, 24]-code) | [i] | ✔ | |
| 10 | Linear OA(5136, 78153, F5, 23) (dual of [78153, 78017, 24]-code) | [i] | ✔ | |
| 11 | Linear OA(5137, 78164, F5, 23) (dual of [78164, 78027, 24]-code) | [i] | ✔ | |
| 12 | Linear OA(5134, 78152, F5, 22) (dual of [78152, 78018, 23]-code) | [i] | ✔ | |
| 13 | Linear OA(5135, 78162, F5, 22) (dual of [78162, 78027, 23]-code) | [i] | ✔ | |
| 14 | Linear OA(5103, 78152, F5, 17) (dual of [78152, 78049, 18]-code) | [i] | ✔ | |
| 15 | Linear OA(5104, 78159, F5, 17) (dual of [78159, 78055, 18]-code) | [i] | ✔ | |
| 16 | Linear OA(5136, 78163, F5, 23) (dual of [78163, 78027, 24]-code) | [i] | ✔ | |