Information on Result #611553
Linear OA(328, 19683, F3, 5) (dual of [19683, 19655, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5
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(328, 17881, F3, 2, 5) (dual of [(17881, 2), 35734, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(328, 17881, F3, 3, 5) (dual of [(17881, 3), 53615, 6]-NRT-code) | [i] | ||
| 3 | Linear OOA(328, 17881, F3, 4, 5) (dual of [(17881, 4), 71496, 6]-NRT-code) | [i] | ||
| 4 | Linear OA(338, 19693, F3, 7) (dual of [19693, 19655, 8]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 5 | Linear OA(350, 19705, F3, 8) (dual of [19705, 19655, 9]-code) | [i] | ✔ | |
| 6 | Linear OA(349, 19697, F3, 8) (dual of [19697, 19648, 9]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 7 | Linear OA(340, 19697, F3, 7) (dual of [19697, 19657, 8]-code) | [i] | ✔ | |
| 8 | Linear OA(338, 19694, F3, 7) (dual of [19694, 19656, 8]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |