Information on Result #613607
Linear OA(549, 390625, F5, 8) (dual of [390625, 390576, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, 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(553, 390631, F5, 8) (dual of [390631, 390578, 9]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(554, 390636, F5, 8) (dual of [390636, 390582, 9]-code) | [i] | ||
| 3 | Linear OOA(549, 292359, F5, 2, 8) (dual of [(292359, 2), 584669, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(549, 292359, F5, 3, 8) (dual of [(292359, 3), 877028, 9]-NRT-code) | [i] | ||
| 5 | Digital (41, 49, 292359)-net over F5 | [i] | ||
| 6 | Linear OA(554, 390631, F5, 8) (dual of [390631, 390577, 9]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 7 | Linear OA(557, 390633, F5, 9) (dual of [390633, 390576, 10]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(549, 390633, F5, 8) (dual of [390633, 390584, 9]-code) | [i] | ✔ | |
| 9 | Linear OA(566, 390642, F5, 10) (dual of [390642, 390576, 11]-code) | [i] | ✔ | |
| 10 | Linear OA(568, 390644, F5, 11) (dual of [390644, 390576, 12]-code) | [i] | ✔ | |
| 11 | Linear OA(550, 390642, F5, 8) (dual of [390642, 390592, 9]-code) | [i] | ✔ | |
| 12 | Linear OA(577, 390651, F5, 12) (dual of [390651, 390574, 13]-code) | [i] | ✔ | |
| 13 | Linear OA(578, 390654, F5, 12) (dual of [390654, 390576, 13]-code) | [i] | ✔ | |
| 14 | Linear OA(553, 390651, F5, 8) (dual of [390651, 390598, 9]-code) | [i] | ✔ | |
| 15 | Linear OA(554, 390654, F5, 8) (dual of [390654, 390600, 9]-code) | [i] | ✔ | |
| 16 | Linear OA(589, 390665, F5, 13) (dual of [390665, 390576, 14]-code) | [i] | ✔ | |
| 17 | Linear OA(599, 390675, F5, 14) (dual of [390675, 390576, 15]-code) | [i] | ✔ | |
| 18 | Linear OA(588, 390664, F5, 13) (dual of [390664, 390576, 14]-code) | [i] | ✔ | |
| 19 | Linear OA(598, 390669, F5, 14) (dual of [390669, 390571, 15]-code) | [i] | ✔ | |
| 20 | Linear OA(598, 390671, F5, 14) (dual of [390671, 390573, 15]-code) | [i] | ✔ | |
| 21 | Linear OA(598, 390674, F5, 14) (dual of [390674, 390576, 15]-code) | [i] | ✔ | |
| 22 | Linear OA(588, 390658, F5, 13) (dual of [390658, 390570, 14]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 23 | Linear OA(587, 390656, F5, 13) (dual of [390656, 390569, 14]-code) | [i] | ✔ | |
| 24 | Linear OA(580, 390658, F5, 12) (dual of [390658, 390578, 13]-code) | [i] | ✔ | |
| 25 | Linear OA(579, 390656, F5, 12) (dual of [390656, 390577, 13]-code) | [i] | ✔ | |
| 26 | Linear OA(567, 390636, F5, 11) (dual of [390636, 390569, 12]-code) | [i] | ✔ | |
| 27 | Linear OA(550, 390635, F5, 8) (dual of [390635, 390585, 9]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 28 | Linear OA(566, 390643, F5, 10) (dual of [390643, 390577, 11]-code) | [i] | ✔ | |
| 29 | Linear OA(550, 390643, F5, 8) (dual of [390643, 390593, 9]-code) | [i] | ✔ | |