Information on Result #629177
Linear OA(1628, 514, F16, 14) (dual of [514, 486, 15]-code), using trace code based on linear OA(25614, 257, F256, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using
- extended Reed–Solomon code RSe(243,256) [i]
- algebraic-geometric code AG(F,121P) 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 = 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+48P) with degQ = 2 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(1629, 515, F16, 14) (dual of [515, 486, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1635, 531, F16, 14) (dual of [531, 496, 15]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1636, 538, F16, 14) (dual of [538, 502, 15]-code) | [i] | ||
| 4 | Linear OA(1637, 547, F16, 14) (dual of [547, 510, 15]-code) | [i] | ||
| 5 | Linear OA(1638, 552, F16, 14) (dual of [552, 514, 15]-code) | [i] | ||
| 6 | Linear OA(1635, 686, F16, 14) (dual of [686, 651, 15]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(1636, 828, F16, 14) (dual of [828, 792, 15]-code) | [i] | ||
| 8 | Linear OA(1637, 1018, F16, 14) (dual of [1018, 981, 15]-code) | [i] | ||
| 9 | Linear OOA(1628, 257, F16, 2, 14) (dual of [(257, 2), 486, 15]-NRT-code) | [i] | OOA Folding | |