Information on Result #682106
Linear OA(5127, 1953126, F5, 17) (dual of [1953126, 1952999, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, 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(5127, 1194128, F5, 2, 17) (dual of [(1194128, 2), 2388129, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5127, 1194128, F5, 3, 17) (dual of [(1194128, 3), 3582257, 18]-NRT-code) | [i] | ||
| 3 | Digital (110, 127, 1194128)-net over F5 | [i] | ||
| 4 | Linear OA(5146, 1953145, F5, 19) (dual of [1953145, 1952999, 20]-code) | [i] | ✔ | Construction X with Cyclic Codes |
| 5 | Linear OA(5148, 1953132, F5, 21) (dual of [1953132, 1952984, 22]-code) | [i] | ✔ | |
| 6 | Linear OA(5149, 1953148, F5, 21) (dual of [1953148, 1952999, 22]-code) | [i] | ✔ | |
| 7 | Linear OA(5147, 1953132, F5, 20) (dual of [1953132, 1952985, 21]-code) | [i] | ✔ | |
| 8 | Linear OA(5128, 1953145, F5, 17) (dual of [1953145, 1953017, 18]-code) | [i] | ✔ | |
| 9 | Linear OA(5146, 1953146, F5, 19) (dual of [1953146, 1953000, 20]-code) | [i] | ✔ | Construction X4 with Cyclic Codes |
| 10 | Linear OA(5128, 1953146, F5, 17) (dual of [1953146, 1953018, 18]-code) | [i] | ✔ | |