Information on Result #617421
Linear OA(2722, 19683, F27, 8) (dual of [19683, 19661, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8
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(2726, 19711, F27, 8) (dual of [19711, 19685, 9]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2727, 19721, F27, 8) (dual of [19721, 19694, 9]-code) | [i] | ||
| 3 | Linear OA(2728, 20385, F27, 8) (dual of [20385, 20357, 9]-code) | [i] | ||
| 4 | Linear OOA(2722, 11774, F27, 2, 8) (dual of [(11774, 2), 23526, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (14, 22, 11774)-net over F27 | [i] | ||
| 6 | Linear OA(2727, 19689, F27, 8) (dual of [19689, 19662, 9]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 7 | Linear OA(2728, 19739, F27, 8) (dual of [19739, 19711, 9]-code) | [i] | ||
| 8 | Linear OA(2725, 19686, F27, 9) (dual of [19686, 19661, 10]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 9 | Linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code) | [i] | ✔ | |
| 10 | Linear OA(2729, 19690, F27, 10) (dual of [19690, 19661, 11]-code) | [i] | ✔ | |
| 11 | Linear OA(2723, 19690, F27, 8) (dual of [19690, 19667, 9]-code) | [i] | ✔ | |
| 12 | Linear OA(2733, 19694, F27, 11) (dual of [19694, 19661, 12]-code) | [i] | ✔ | |
| 13 | Linear OA(2724, 19694, F27, 8) (dual of [19694, 19670, 9]-code) | [i] | ✔ | |
| 14 | Linear OA(2737, 19698, F27, 12) (dual of [19698, 19661, 13]-code) | [i] | ✔ | |
| 15 | Linear OA(2725, 19698, F27, 8) (dual of [19698, 19673, 9]-code) | [i] | ✔ | |
| 16 | Linear OA(2741, 19702, F27, 13) (dual of [19702, 19661, 14]-code) | [i] | ✔ | |
| 17 | Linear OA(2745, 19706, F27, 14) (dual of [19706, 19661, 15]-code) | [i] | ✔ | |
| 18 | Linear OA(2749, 19710, F27, 15) (dual of [19710, 19661, 16]-code) | [i] | ✔ | |
| 19 | Linear OA(2754, 19715, F27, 16) (dual of [19715, 19661, 17]-code) | [i] | ✔ | |
| 20 | Linear OA(2753, 19712, F27, 16) (dual of [19712, 19659, 17]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 21 | Linear OA(2732, 19694, F27, 10) (dual of [19694, 19662, 11]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |