Information on Result #662927
Linear OA(5137, 1953137, F5, 18) (dual of [1953137, 1953000, 19]-code), using (u, u+v)-construction based on
- linear OA(510, 12, F5, 9) (dual of [12, 2, 10]-code), using
- repeating each code word 2 times [i] based on linear OA(54, 6, F5, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
- extended Reed–Solomon code RSe(2,5) [i]
- Simplex code S(2,5) [i]
- repeating each code word 2 times [i] based on linear OA(54, 6, F5, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
- linear OA(5127, 1953125, F5, 18) (dual of [1953125, 1952998, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
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(5137, 1484980, F5, 2, 18) (dual of [(1484980, 2), 2969823, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5137, 1484980, F5, 3, 18) (dual of [(1484980, 3), 4454803, 19]-NRT-code) | [i] | ||
| 3 | Digital (119, 137, 1484980)-net over F5 | [i] | ||