Information on Result #895594
Linear OOA(4153, 4194306, F4, 2, 17) (dual of [(4194306, 2), 8388459, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(48, 5, F4, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;2,4) [i]
- linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4153, 4194306, F4, 3, 17) (dual of [(4194306, 3), 12582765, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (136, 153, 4194306)-net over F4 | [i] | ||
| 3 | Linear OOA(4153, 1048576, F4, 18, 17) (dual of [(1048576, 18), 18874215, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |