Information on Result #682331
Linear OA(570, 390662, F5, 10) (dual of [390662, 390592, 11]-code), using construction X applied to Ce(10) ⊂ Ce(5) based on
- linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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 [i]
- linear OA(55, 37, F5, 3) (dual of [37, 32, 4]-code or 37-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(570, 390662, F5, 2, 10) (dual of [(390662, 2), 781254, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(570, 390662, F5, 3, 10) (dual of [(390662, 3), 1171916, 11]-NRT-code) | [i] | ||
| 3 | Digital (60, 70, 390662)-net over F5 | [i] | ||
| 4 | Linear OA(571, 390664, F5, 10) (dual of [390664, 390593, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(570, 195331, F5, 2, 10) (dual of [(195331, 2), 390592, 11]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(570, 130220, F5, 3, 10) (dual of [(130220, 3), 390590, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(570, 78132, F5, 10, 10) (dual of [(78132, 10), 781250, 11]-NRT-code) | [i] | OA Folding and Stacking | |