Information on Result #629174
Linear OA(1624, 514, F16, 12) (dual of [514, 490, 13]-code), using trace code based on linear OA(25612, 257, F256, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using
- extended Reed–Solomon code RSe(245,256) [i]
- algebraic-geometric code AG(F,122P) 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, Q+80P) with degQ = 4 and 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+48P) 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(1625, 515, F16, 12) (dual of [515, 490, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1630, 531, F16, 12) (dual of [531, 501, 13]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1631, 538, F16, 12) (dual of [538, 507, 13]-code) | [i] | ||
| 4 | Linear OA(1632, 547, F16, 12) (dual of [547, 515, 13]-code) | [i] | ||
| 5 | Linear OA(1630, 668, F16, 12) (dual of [668, 638, 13]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(1631, 824, F16, 12) (dual of [824, 793, 13]-code) | [i] | ||
| 7 | Linear OA(1632, 1049, F16, 12) (dual of [1049, 1017, 13]-code) | [i] | ||
| 8 | Linear OOA(1624, 257, F16, 2, 12) (dual of [(257, 2), 490, 13]-NRT-code) | [i] | OOA Folding | |