Information on Result #612208
Linear OA(3235, 19703, F3, 37) (dual of [19703, 19468, 38]-code), using construction X applied to C([0,18]) ⊂ C([1,18]) based on
- 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(3216, 19684, F3, 18) (dual of [19684, 19468, 19]-code), using the narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(318, 19, F3, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,3)), using
- dual of repetition code with length 19 [i]
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, 10734, F3, 2, 37) (dual of [(10734, 2), 21233, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3235, 10734, F3, 3, 37) (dual of [(10734, 3), 31967, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3235, 10734, F3, 4, 37) (dual of [(10734, 4), 42701, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3235, 10734, F3, 5, 37) (dual of [(10734, 5), 53435, 38]-NRT-code) | [i] | ||
| 5 | Digital (198, 235, 10734)-net over F3 | [i] | ||