Information on Result #629190
Linear OA(1644, 514, F16, 22) (dual of [514, 470, 23]-code), using trace code based on linear OA(25622, 257, F256, 22) (dual of [257, 235, 23]-code or 257-arc in PG(21,256)), using
- extended Reed–Solomon code RSe(235,256) [i]
- algebraic-geometric code AG(F,117P) 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,78P) 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+46P) with degQ = 4 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(1645, 515, F16, 22) (dual of [515, 470, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1657, 547, F16, 22) (dual of [547, 490, 23]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1658, 552, F16, 22) (dual of [552, 494, 23]-code) | [i] | ||
| 4 | Linear OA(1659, 559, F16, 22) (dual of [559, 500, 23]-code) | [i] | ||
| 5 | Linear OA(1653, 654, F16, 22) (dual of [654, 601, 23]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(1654, 736, F16, 22) (dual of [736, 682, 23]-code) | [i] | ||
| 7 | Linear OOA(1644, 257, F16, 2, 22) (dual of [(257, 2), 470, 23]-NRT-code) | [i] | OOA Folding | |