Information on Result #1021984
Linear OOA(719, 208, F7, 3, 6) (dual of [(208, 3), 605, 7]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(72, 8, F7, 3, 2) (dual of [(8, 3), 22, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;22,7) [i]
- linear OOA(75, 100, F7, 3, 3) (dual of [(100, 3), 295, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(75, 131, F7, 3, 3) (dual of [(131, 3), 388, 4]-NRT-code), using
- linear OOA(712, 100, F7, 3, 6) (dual of [(100, 3), 288, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 12, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 6, 50)-net over F49, using
- extracting embedded OOA [i] based on digital (6, 12, 100)-net over F7, 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(7109, 3843410, F7, 3, 12) (dual of [(3843410, 3), 11530121, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(719, 207, F7, 9, 6) (dual of [(207, 9), 1844, 7]-NRT-code) | [i] | OOA Stacking with Additional Row | |