Information on Result #682872
Linear OA(5123, 3132, F5, 30) (dual of [3132, 3009, 31]-code), using construction X applied to C([0,15]) ⊂ C([0,13]) based on
- linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(5111, 3126, F5, 27) (dual of [3126, 3015, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [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(5123, 3117, F5, 2, 30) (dual of [(3117, 2), 6111, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5123, 3117, F5, 3, 30) (dual of [(3117, 3), 9228, 31]-NRT-code) | [i] | ||
| 3 | Digital (93, 123, 3117)-net over F5 | [i] | ||