Information on Result #629187
Linear OA(1640, 514, F16, 20) (dual of [514, 474, 21]-code), using trace code based on linear OA(25620, 257, F256, 20) (dual of [257, 237, 21]-code or 257-arc in PG(19,256)), using
- extended Reed–Solomon code RSe(237,256) [i]
- algebraic-geometric code AG(F,118P) 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+78P) 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, Q+46P) with degQ = 6 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(1641, 515, F16, 20) (dual of [515, 474, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1651, 538, F16, 20) (dual of [538, 487, 21]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1652, 547, F16, 20) (dual of [547, 495, 21]-code) | [i] | ||
| 4 | Linear OA(1653, 552, F16, 20) (dual of [552, 499, 21]-code) | [i] | ||
| 5 | Linear OA(1649, 691, F16, 20) (dual of [691, 642, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(1650, 791, F16, 20) (dual of [791, 741, 21]-code) | [i] | ||
| 7 | Linear OOA(1640, 257, F16, 2, 20) (dual of [(257, 2), 474, 21]-NRT-code) | [i] | OOA Folding | |