Information on Result #1081352
Linear OOA(3219, 2097479, F3, 4, 19) (dual of [(2097479, 4), 8389697, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(336, 328, F3, 4, 9) (dual of [(328, 4), 1276, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 36, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 9, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 9, 82)-net over F81, using
- extracting embedded OOA [i] based on digital (27, 36, 328)-net over F3, using
- linear OOA(3183, 2097151, F3, 4, 19) (dual of [(2097151, 4), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3183, 4194302, F3, 2, 19) (dual of [(4194302, 2), 8388421, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 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 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3183, 4194302, F3, 2, 19) (dual of [(4194302, 2), 8388421, 20]-NRT-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(3219, 2097479, F3, 4, 18) (dual of [(2097479, 4), 8389697, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3220, 2097479, F3, 4, 19) (dual of [(2097479, 4), 8389696, 20]-NRT-code) | [i] | OOA Duplication | |