Information on Result #662308
Linear OA(4213, 65559, F4, 33) (dual of [65559, 65346, 34]-code), using (u, u+v)-construction based on
- linear OA(420, 22, F4, 16) (dual of [22, 2, 17]-code), using
- 3 times truncation [i] based on linear OA(423, 25, F4, 19) (dual of [25, 2, 20]-code), using
- repeating each code word 5 times [i] based on linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reed–Solomon code RSe(2,4) [i]
- Simplex code S(2,4) [i]
- repeating each code word 5 times [i] based on linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- 3 times truncation [i] based on linear OA(423, 25, F4, 19) (dual of [25, 2, 20]-code), using
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [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(4213, 54203, F4, 2, 33) (dual of [(54203, 2), 108193, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4213, 54203, F4, 3, 33) (dual of [(54203, 3), 162396, 34]-NRT-code) | [i] | ||
| 3 | Digital (180, 213, 54203)-net over F4 | [i] | ||