Information on Result #675828
Linear OA(3180, 2227, F3, 37) (dual of [2227, 2047, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 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(311, 39, F3, 5) (dual of [39, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 40, F3, 5) (dual of [40, 29, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(37, 14, F3, 5) (dual of [14, 7, 6]-code), using
- extended quadratic residue code Qe(14,3) [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(311, 40, F3, 5) (dual of [40, 29, 6]-code), 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 OA(3180, 2227, F3, 36) (dual of [2227, 2047, 37]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(3180, 1883, F3, 2, 37) (dual of [(1883, 2), 3586, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3180, 1883, F3, 3, 37) (dual of [(1883, 3), 5469, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3180, 1883, F3, 4, 37) (dual of [(1883, 4), 7352, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(3180, 1883, F3, 5, 37) (dual of [(1883, 5), 9235, 38]-NRT-code) | [i] | ||
| 6 | Digital (143, 180, 1883)-net over F3 | [i] | ||
| 7 | Linear OA(3184, 2234, F3, 37) (dual of [2234, 2050, 38]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(3188, 2242, F3, 37) (dual of [2242, 2054, 38]-code) | [i] | ||