Information on Result #671875
Linear OA(25614, 517, F256, 9) (dual of [517, 503, 10]-code), using (u, u+v)-construction based on
- linear OA(2564, 257, F256, 4) (dual of [257, 253, 5]-code or 257-arc in PG(3,256)), using
- extended Reed–Solomon code RSe(253,256) [i]
- algebraic-geometric code AG(F,126P) 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,84P) 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+50P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25610, 260, F256, 9) (dual of [260, 250, 10]-code), using
- construction X applied to AG(F, Q+122P) ⊂ AG(F, Q+123P) [i] based on
- linear OA(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using algebraic-geometric code AG(F, Q+122P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using algebraic-geometric code AG(F, Q+123P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+122P) ⊂ AG(F, Q+123P) [i] based on
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 | OA(12816, 517, S128, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(25651, 66054, F256, 19) (dual of [66054, 66003, 20]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(25649, 66053, F256, 18) (dual of [66053, 66004, 19]-code) | [i] | ||
| 4 | Linear OA(25651, 66055, F256, 19) (dual of [66055, 66004, 20]-code) | [i] | ||
| 5 | Linear OA(25649, 66055, F256, 18) (dual of [66055, 66006, 19]-code) | [i] | ||