Information on Result #1313625
Linear OA(1632, 1049, F16, 12) (dual of [1049, 1017, 13]-code), using 527 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 39 times 0, 1, 89 times 0, 1, 154 times 0, 1, 223 times 0) based on linear OA(1624, 514, F16, 12) (dual of [514, 490, 13]-code), using
- trace code [i] based on linear OA(25612, 257, F256, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using
- extended Reed–Solomon code RSe(245,256) [i]
- algebraic-geometric code AG(F,122P) 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 = 4 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 = 4 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
Mode: 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 OOA(1632, 1049, F16, 2, 12) (dual of [(1049, 2), 2066, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (20, 32, 1049)-net over F16 | [i] | ||