Information on Result #682314
Linear OA(578, 390654, F5, 12) (dual of [390654, 390576, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) based on
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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 [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(578, 272882, F5, 2, 12) (dual of [(272882, 2), 545686, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 272882, F5, 3, 12) (dual of [(272882, 3), 818568, 13]-NRT-code) | [i] | ||
| 3 | Digital (66, 78, 272882)-net over F5 | [i] | ||
| 4 | Linear OOA(578, 195327, F5, 2, 12) (dual of [(195327, 2), 390576, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(578, 130218, F5, 3, 12) (dual of [(130218, 3), 390576, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(578, 65109, F5, 12, 12) (dual of [(65109, 12), 781230, 13]-NRT-code) | [i] | OA Folding and Stacking | |