Information on Result #675305
Linear OA(3210, 6579, F3, 39) (dual of [6579, 6369, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,18]) based on
- linear OA(3209, 6562, F3, 39) (dual of [6562, 6353, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 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 OA(3211, 6580, F3, 39) (dual of [6580, 6369, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3212, 6581, F3, 39) (dual of [6581, 6369, 40]-code) | [i] | ||
| 3 | Linear OOA(3210, 3595, F3, 2, 39) (dual of [(3595, 2), 6980, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3210, 3595, F3, 3, 39) (dual of [(3595, 3), 10575, 40]-NRT-code) | [i] | ||
| 5 | Linear OOA(3210, 3595, F3, 4, 39) (dual of [(3595, 4), 14170, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(3210, 3595, F3, 5, 39) (dual of [(3595, 5), 17765, 40]-NRT-code) | [i] | ||
| 7 | Digital (171, 210, 3595)-net over F3 | [i] | ||
| 8 | Linear OOA(3210, 3289, F3, 2, 39) (dual of [(3289, 2), 6368, 40]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3210, 2193, F3, 3, 39) (dual of [(2193, 3), 6369, 40]-NRT-code) | [i] | ||
| 10 | Linear OOA(3210, 1644, F3, 4, 39) (dual of [(1644, 4), 6366, 40]-NRT-code) | [i] | ||
| 11 | Linear OOA(3210, 1315, F3, 5, 39) (dual of [(1315, 5), 6365, 40]-NRT-code) | [i] | ||