Information on Result #629197
Linear OA(1652, 514, F16, 26) (dual of [514, 462, 27]-code), using trace code based on linear OA(25626, 257, F256, 26) (dual of [257, 231, 27]-code or 257-arc in PG(25,256)), using
- extended Reed–Solomon code RSe(231,256) [i]
- algebraic-geometric code AG(F,115P) 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+76P) with degQ = 2 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,46P) with 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(1653, 515, F16, 26) (dual of [515, 462, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1667, 547, F16, 26) (dual of [547, 480, 27]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1668, 552, F16, 26) (dual of [552, 484, 27]-code) | [i] | ||
| 4 | Linear OA(1669, 559, F16, 26) (dual of [559, 490, 27]-code) | [i] | ||
| 5 | Linear OA(1670, 563, F16, 26) (dual of [563, 493, 27]-code) | [i] | ||
| 6 | Linear OA(1671, 579, F16, 26) (dual of [579, 508, 27]-code) | [i] | ||
| 7 | Linear OA(1662, 673, F16, 26) (dual of [673, 611, 27]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(1663, 748, F16, 26) (dual of [748, 685, 27]-code) | [i] | ||
| 9 | Linear OOA(1652, 257, F16, 2, 26) (dual of [(257, 2), 462, 27]-NRT-code) | [i] | OOA Folding | |