Information on Result #613584
Linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, 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(528, 78124, F5, 5) (dual of [78124, 78096, 6]-code) | [i] | Truncation | |
| 2 | Linear OA(532, 78131, F5, 6) (dual of [78131, 78099, 7]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(529, 43228, F5, 2, 6) (dual of [(43228, 2), 86427, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(529, 43228, F5, 3, 6) (dual of [(43228, 3), 129655, 7]-NRT-code) | [i] | ||
| 5 | Digital (23, 29, 43228)-net over F5 | [i] | ||
| 6 | Linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 7 | Linear OA(530, 78133, F5, 6) (dual of [78133, 78103, 7]-code) | [i] | ✔ | |
| 8 | Linear OA(544, 78140, F5, 8) (dual of [78140, 78096, 9]-code) | [i] | ✔ | |
| 9 | Linear OA(532, 78142, F5, 6) (dual of [78142, 78110, 7]-code) | [i] | ✔ | |
| 10 | Linear OA(553, 78149, F5, 9) (dual of [78149, 78096, 10]-code) | [i] | ✔ | |
| 11 | Linear OA(561, 78151, F5, 10) (dual of [78151, 78090, 11]-code) | [i] | ✔ | |
| 12 | Linear OA(562, 78158, F5, 10) (dual of [78158, 78096, 11]-code) | [i] | ✔ | |
| 13 | Linear OA(563, 78155, F5, 11) (dual of [78155, 78092, 12]-code) | [i] | ✔ | |
| 14 | Linear OA(564, 78160, F5, 11) (dual of [78160, 78096, 12]-code) | [i] | ✔ | |
| 15 | Linear OA(564, 78155, F5, 11) (dual of [78155, 78091, 12]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 16 | Linear OA(562, 78152, F5, 11) (dual of [78152, 78090, 12]-code) | [i] | ✔ | |
| 17 | Linear OA(556, 78154, F5, 9) (dual of [78154, 78098, 10]-code) | [i] | ✔ | |
| 18 | Linear OA(555, 78152, F5, 9) (dual of [78152, 78097, 10]-code) | [i] | ✔ | |
| 19 | Linear OA(537, 78134, F5, 7) (dual of [78134, 78097, 8]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 20 | Linear OA(530, 78134, F5, 6) (dual of [78134, 78104, 7]-code) | [i] | ✔ | |
| 21 | Linear OA(544, 78141, F5, 8) (dual of [78141, 78097, 9]-code) | [i] | ✔ | |
| 22 | Linear OOA(529, 39062, F5, 2, 6) (dual of [(39062, 2), 78095, 7]-NRT-code) | [i] | OOA Folding | |
| 23 | Linear OOA(529, 26041, F5, 3, 6) (dual of [(26041, 3), 78094, 7]-NRT-code) | [i] | ||
| 24 | Linear OOA(529, 26041, F5, 6, 6) (dual of [(26041, 6), 156217, 7]-NRT-code) | [i] | OA Folding and Stacking | |