Information on Result #629205
Linear OA(1662, 514, F16, 31) (dual of [514, 452, 32]-code), using trace code based on linear OA(25631, 257, F256, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using
- extended Reed–Solomon code RSe(226,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+111P) with degQ = 3 and 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,75P) with 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,45P) 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(1663, 515, F16, 31) (dual of [515, 452, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1681, 559, F16, 31) (dual of [559, 478, 32]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1682, 563, F16, 31) (dual of [563, 481, 32]-code) | [i] | ||
| 4 | Linear OA(1683, 579, F16, 31) (dual of [579, 496, 32]-code) | [i] | ||
| 5 | Linear OA(1684, 581, F16, 31) (dual of [581, 497, 32]-code) | [i] | ||
| 6 | Linear OA(1685, 583, F16, 31) (dual of [583, 498, 32]-code) | [i] | ||
| 7 | Linear OA(1686, 585, F16, 31) (dual of [585, 499, 32]-code) | [i] | ||
| 8 | Linear OA(1673, 699, F16, 31) (dual of [699, 626, 32]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OOA(1662, 257, F16, 2, 31) (dual of [(257, 2), 452, 32]-NRT-code) | [i] | OOA Folding | |