Information on Result #675842
Linear OA(3147, 2222, F3, 29) (dual of [2222, 2075, 30]-code), using construction X applied to C([0,15]) ⊂ C([0,12]) based on
- linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(36, 34, F3, 3) (dual of [34, 28, 4]-code or 34-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
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(3147, 2051, F3, 2, 29) (dual of [(2051, 2), 3955, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3147, 2051, F3, 3, 29) (dual of [(2051, 3), 6006, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3147, 2051, F3, 4, 29) (dual of [(2051, 4), 8057, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3147, 2051, F3, 5, 29) (dual of [(2051, 5), 10108, 30]-NRT-code) | [i] | ||
| 5 | Digital (118, 147, 2051)-net over F3 | [i] | ||