Information on Result #629213
Linear OA(1672, 514, F16, 36) (dual of [514, 442, 37]-code), using trace code based on linear OA(25636, 257, F256, 36) (dual of [257, 221, 37]-code or 257-arc in PG(35,256)), using
- extended Reed–Solomon code RSe(221,256) [i]
- algebraic-geometric code AG(F,110P) 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+72P) 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,44P) 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(1673, 515, F16, 36) (dual of [515, 442, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1695, 563, F16, 36) (dual of [563, 468, 37]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1696, 579, F16, 36) (dual of [579, 483, 37]-code) | [i] | ||
| 4 | Linear OA(1697, 581, F16, 36) (dual of [581, 484, 37]-code) | [i] | ||
| 5 | Linear OA(1698, 583, F16, 36) (dual of [583, 485, 37]-code) | [i] | ||
| 6 | Linear OA(1683, 683, F16, 36) (dual of [683, 600, 37]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(1672, 257, F16, 2, 36) (dual of [(257, 2), 442, 37]-NRT-code) | [i] | OOA Folding | |