Information on Result #682304
Linear OA(5118, 390654, F5, 18) (dual of [390654, 390536, 19]-code), using construction X applied to Ce(17) ⊂ Ce(13) based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(5118, 219622, F5, 2, 18) (dual of [(219622, 2), 439126, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5118, 219622, F5, 3, 18) (dual of [(219622, 3), 658748, 19]-NRT-code) | [i] | ||
| 3 | Digital (100, 118, 219622)-net over F5 | [i] | ||
| 4 | Linear OOA(5118, 195327, F5, 2, 18) (dual of [(195327, 2), 390536, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5118, 130218, F5, 3, 18) (dual of [(130218, 3), 390536, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(5118, 43406, F5, 18, 18) (dual of [(43406, 18), 781190, 19]-NRT-code) | [i] | OA Folding and Stacking | |