Information on Result #816151
Linear OOA(3236, 9851, F3, 2, 39) (dual of [(9851, 2), 19466, 40]-NRT-code), using OOA 2-folding based on linear OA(3236, 19702, F3, 39) (dual of [19702, 19466, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 19703, F3, 39) (dual of [19703, 19467, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(3235, 19684, F3, 39) (dual of [19684, 19449, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(3217, 19684, F3, 37) (dual of [19684, 19467, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 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
- construction X applied to C([0,19]) ⊂ C([0,18]) [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(3236, 8981, F3, 3, 39) (dual of [(8981, 3), 26707, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3236, 8981, F3, 4, 39) (dual of [(8981, 4), 35688, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3236, 8981, F3, 5, 39) (dual of [(8981, 5), 44669, 40]-NRT-code) | [i] | ||
| 4 | Digital (197, 236, 8981)-net over F3 | [i] | ||