Information on Result #1117810
Linear OOA(3211, 1677834, F3, 5, 19) (dual of [(1677834, 5), 8388959, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(330, 114, F3, 5, 9) (dual of [(114, 5), 540, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (21, 30, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 10, 38)-net over F27, using
- extracting embedded OOA [i] based on digital (21, 30, 114)-net over F3, using
- linear OOA(3181, 1677720, F3, 5, 19) (dual of [(1677720, 5), 8388419, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3181, 8388600, F3, 19) (dual of [8388600, 8388419, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 5-folding [i] based on linear OA(3181, 8388600, F3, 19) (dual of [8388600, 8388419, 20]-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(3211, 1677834, F3, 5, 18) (dual of [(1677834, 5), 8388959, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3212, 1677834, F3, 5, 19) (dual of [(1677834, 5), 8388958, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3213, 1677834, F3, 5, 19) (dual of [(1677834, 5), 8388957, 20]-NRT-code) | [i] | ||