Information on Result #675805
Linear OA(3235, 2224, F3, 49) (dual of [2224, 1989, 50]-code), using construction X applied to C([0,24]) ⊂ C([0,21]) based on
- linear OA(3225, 2188, F3, 49) (dual of [2188, 1963, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- 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(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
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(3235, 2137, F3, 2, 49) (dual of [(2137, 2), 4039, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3235, 2137, F3, 3, 49) (dual of [(2137, 3), 6176, 50]-NRT-code) | [i] | ||
| 3 | Linear OOA(3235, 2137, F3, 4, 49) (dual of [(2137, 4), 8313, 50]-NRT-code) | [i] | ||
| 4 | Linear OOA(3235, 2137, F3, 5, 49) (dual of [(2137, 5), 10450, 50]-NRT-code) | [i] | ||
| 5 | Digital (186, 235, 2137)-net over F3 | [i] | ||
| 6 | Linear OOA(3235, 556, F3, 4, 49) (dual of [(556, 4), 1989, 50]-NRT-code) | [i] | OOA Folding | |