Information on Result #682312
Linear OA(586, 390654, F5, 13) (dual of [390654, 390568, 14]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
- linear OA(581, 390625, F5, 13) (dual of [390625, 390544, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(557, 390625, F5, 9) (dual of [390625, 390568, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
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(586, 309084, F5, 2, 13) (dual of [(309084, 2), 618082, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(586, 309084, F5, 3, 13) (dual of [(309084, 3), 927166, 14]-NRT-code) | [i] | ||
| 3 | Digital (73, 86, 309084)-net over F5 | [i] | ||
| 4 | Linear OOA(586, 195327, F5, 2, 13) (dual of [(195327, 2), 390568, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(586, 130218, F5, 3, 13) (dual of [(130218, 3), 390568, 14]-NRT-code) | [i] | ||