Information on Result #629215
Linear OA(1674, 514, F16, 37) (dual of [514, 440, 38]-code), using trace code based on linear OA(25637, 257, F256, 37) (dual of [257, 220, 38]-code or 257-arc in PG(36,256)), using
- extended Reed–Solomon code RSe(220,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+108P) 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,73P) 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, Q+43P) with degQ = 4 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(1675, 515, F16, 37) (dual of [515, 440, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1697, 563, F16, 37) (dual of [563, 466, 38]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1698, 579, F16, 37) (dual of [579, 481, 38]-code) | [i] | ||
| 4 | Linear OA(1699, 581, F16, 37) (dual of [581, 482, 38]-code) | [i] | ||
| 5 | Linear OA(16100, 583, F16, 37) (dual of [583, 483, 38]-code) | [i] | ||
| 6 | Linear OA(16101, 585, F16, 37) (dual of [585, 484, 38]-code) | [i] | ||
| 7 | Linear OA(1685, 682, F16, 37) (dual of [682, 597, 38]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(1686, 735, F16, 37) (dual of [735, 649, 38]-code) | [i] | ||
| 9 | Linear OOA(1674, 257, F16, 2, 37) (dual of [(257, 2), 440, 38]-NRT-code) | [i] | OOA Folding | |