Information on Result #613585
Linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6
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(532, 390624, F5, 5) (dual of [390624, 390592, 6]-code) | [i] | Truncation | |
| 2 | Linear OA(536, 390631, F5, 6) (dual of [390631, 390595, 7]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(533, 216147, F5, 2, 6) (dual of [(216147, 2), 432261, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(533, 216147, F5, 3, 6) (dual of [(216147, 3), 648408, 7]-NRT-code) | [i] | ||
| 5 | Digital (27, 33, 216147)-net over F5 | [i] | ||
| 6 | Linear OA(541, 390633, F5, 7) (dual of [390633, 390592, 8]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 7 | Linear OA(534, 390634, F5, 6) (dual of [390634, 390600, 7]-code) | [i] | ✔ | |
| 8 | Linear OA(550, 390642, F5, 8) (dual of [390642, 390592, 9]-code) | [i] | ✔ | |
| 9 | Linear OA(536, 390644, F5, 6) (dual of [390644, 390608, 7]-code) | [i] | ✔ | |
| 10 | Linear OA(560, 390652, F5, 9) (dual of [390652, 390592, 10]-code) | [i] | ✔ | |
| 11 | Linear OA(570, 390662, F5, 10) (dual of [390662, 390592, 11]-code) | [i] | ✔ | |
| 12 | Linear OA(572, 390664, F5, 11) (dual of [390664, 390592, 12]-code) | [i] | ✔ | |
| 13 | Linear OA(572, 390658, F5, 11) (dual of [390658, 390586, 12]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 14 | Linear OA(571, 390656, F5, 11) (dual of [390656, 390585, 12]-code) | [i] | ✔ | |
| 15 | Linear OA(569, 390654, F5, 10) (dual of [390654, 390585, 11]-code) | [i] | ✔ | |
| 16 | Linear OA(563, 390657, F5, 9) (dual of [390657, 390594, 10]-code) | [i] | ✔ | |
| 17 | Linear OA(562, 390655, F5, 9) (dual of [390655, 390593, 10]-code) | [i] | ✔ | |
| 18 | Linear OA(542, 390635, F5, 7) (dual of [390635, 390593, 8]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 19 | Linear OA(534, 390635, F5, 6) (dual of [390635, 390601, 7]-code) | [i] | ✔ | |
| 20 | Linear OA(550, 390643, F5, 8) (dual of [390643, 390593, 9]-code) | [i] | ✔ | |
| 21 | Linear OOA(533, 195312, F5, 2, 6) (dual of [(195312, 2), 390591, 7]-NRT-code) | [i] | OOA Folding | |
| 22 | Linear OOA(533, 130208, F5, 3, 6) (dual of [(130208, 3), 390591, 7]-NRT-code) | [i] | ||
| 23 | Linear OOA(533, 130208, F5, 6, 6) (dual of [(130208, 6), 781215, 7]-NRT-code) | [i] | OA Folding and Stacking | |