Information on Result #1021998
Linear OOA(823, 406, F8, 3, 7) (dual of [(406, 3), 1195, 8]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(81, 73, F8, 3, 1) (dual of [(73, 3), 218, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81, s, F8, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(81, s, F8, 3, 1) for arbitrarily large s, using
- linear OOA(83, 73, F8, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- Hamming code H(3,8) [i]
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- linear OOA(85, 130, F8, 3, 3) (dual of [(130, 3), 385, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(85, 207, F8, 3, 3) (dual of [(207, 3), 616, 4]-NRT-code), using
- linear OOA(814, 130, F8, 3, 7) (dual of [(130, 3), 376, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F8, 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(8137, 5592808, F8, 3, 15) (dual of [(5592808, 3), 16778287, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8129, 5592808, F8, 3, 14) (dual of [(5592808, 3), 16778295, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(823, 405, F8, 9, 7) (dual of [(405, 9), 3622, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |