Information on Result #629212
Linear OA(1670, 514, F16, 35) (dual of [514, 444, 36]-code), using trace code based on linear OA(25635, 257, F256, 35) (dual of [257, 222, 36]-code or 257-arc in PG(34,256)), using
- extended Reed–Solomon code RSe(222,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+109P) 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, Q+73P) 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+43P) 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(1671, 515, F16, 35) (dual of [515, 444, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1691, 559, F16, 35) (dual of [559, 468, 36]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1692, 563, F16, 35) (dual of [563, 471, 36]-code) | [i] | ||
| 4 | Linear OA(1693, 579, F16, 35) (dual of [579, 486, 36]-code) | [i] | ||
| 5 | Linear OA(1694, 581, F16, 35) (dual of [581, 487, 36]-code) | [i] | ||
| 6 | Linear OA(1695, 583, F16, 35) (dual of [583, 488, 36]-code) | [i] | ||
| 7 | Linear OOA(1670, 257, F16, 2, 35) (dual of [(257, 2), 444, 36]-NRT-code) | [i] | OOA Folding | |