Information on Result #629209
Linear OA(1668, 514, F16, 34) (dual of [514, 446, 35]-code), using trace code based on linear OA(25634, 257, F256, 34) (dual of [257, 223, 35]-code or 257-arc in PG(33,256)), using
- extended Reed–Solomon code RSe(223,256) [i]
- algebraic-geometric code AG(F,111P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- algebraic-geometric code AG(F,74P) with degPÂ =Â 3 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+44P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
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 OA(1669, 515, F16, 34) (dual of [515, 446, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1689, 559, F16, 34) (dual of [559, 470, 35]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1690, 563, F16, 34) (dual of [563, 473, 35]-code) | [i] | ||
| 4 | Linear OA(1691, 579, F16, 34) (dual of [579, 488, 35]-code) | [i] | ||
| 5 | Linear OA(1692, 581, F16, 34) (dual of [581, 489, 35]-code) | [i] | ||
| 6 | Linear OA(1679, 687, F16, 34) (dual of [687, 608, 35]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(1668, 257, F16, 2, 34) (dual of [(257, 2), 446, 35]-NRT-code) | [i] | OOA Folding | |