Information on Result #895597
Linear OOA(4156, 4194315, F4, 2, 17) (dual of [(4194315, 2), 8388474, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(411, 14, F4, 2, 8) (dual of [(14, 2), 17, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,19P) [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- 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(4156, 4194315, F4, 3, 17) (dual of [(4194315, 3), 12582789, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (139, 156, 4194315)-net over F4 | [i] | ||
| 3 | Linear OOA(4156, 1048578, F4, 18, 17) (dual of [(1048578, 18), 18874248, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |