Information on Result #614005
Linear OA(5146, 3125, F5, 37) (dual of [3125, 2979, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37
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(5146, 2710, F5, 2, 37) (dual of [(2710, 2), 5274, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5146, 2710, F5, 3, 37) (dual of [(2710, 3), 7984, 38]-NRT-code) | [i] | ||
| 3 | Digital (109, 146, 2710)-net over F5 | [i] | ||
| 4 | Linear OA(5146, 3130, F5, 37) (dual of [3130, 2984, 38]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 5 | Linear OA(5149, 3138, F5, 37) (dual of [3138, 2989, 38]-code) | [i] | ✔ | |
| 6 | Linear OA(5150, 3144, F5, 37) (dual of [3144, 2994, 38]-code) | [i] | ✔ | |
| 7 | Linear OA(5148, 3133, F5, 37) (dual of [3133, 2985, 38]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |