Information on Result #906685
Linear OOA(924, 738, F9, 2, 7) (dual of [(738, 2), 1452, 8]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(90, 82, F9, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(90, s, F9, 2, 0) for arbitrarily large s, using
- linear OOA(90, 82, F9, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
- linear OOA(91, 82, F9, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 2, 1) for arbitrarily large s, using
- linear OOA(91, 82, F9, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
- linear OOA(91, 82, F9, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
- linear OOA(91, 82, F9, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
- linear OOA(93, 82, F9, 2, 2) (dual of [(82, 2), 161, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- Hamming code H(3,9) [i]
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- linear OOA(94, 82, F9, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
- linear OOA(913, 82, F9, 2, 7) (dual of [(82, 2), 151, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) for nets [i] based on digital (0, 7, 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
- base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) for nets [i] based on digital (0, 7, 82)-net over F81, using
- extracting embedded OOA [i] based on digital (6, 13, 82)-net over F9, 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(924, 369, F9, 3, 7) (dual of [(369, 3), 1083, 8]-NRT-code) | [i] | OOA Folding | |