Information on Result #675817
Linear OA(3208, 2227, F3, 43) (dual of [2227, 2019, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,18]) based on
- linear OA(3197, 2188, F3, 43) (dual of [2188, 1991, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- 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(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(3208, 2227, F3, 42) (dual of [2227, 2019, 43]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(3208, 2031, F3, 2, 43) (dual of [(2031, 2), 3854, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3208, 2031, F3, 3, 43) (dual of [(2031, 3), 5885, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3208, 2031, F3, 4, 43) (dual of [(2031, 4), 7916, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(3208, 2031, F3, 5, 43) (dual of [(2031, 5), 9947, 44]-NRT-code) | [i] | ||
| 6 | Digital (165, 208, 2031)-net over F3 | [i] | ||