Information on Result #675769
Linear OA(3142, 2203, F3, 29) (dual of [2203, 2061, 30]-code), using construction X applied to C([0,15]) ⊂ C([0,13]) 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(3127, 2188, F3, 27) (dual of [2188, 2061, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3142, 1669, F3, 2, 29) (dual of [(1669, 2), 3196, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3142, 1669, F3, 3, 29) (dual of [(1669, 3), 4865, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3142, 1669, F3, 4, 29) (dual of [(1669, 4), 6534, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3142, 1669, F3, 5, 29) (dual of [(1669, 5), 8203, 30]-NRT-code) | [i] | ||
| 5 | Digital (113, 142, 1669)-net over F3 | [i] | ||