Information on Result #1313646
Linear OA(1637, 1018, F16, 14) (dual of [1018, 981, 15]-code), using 495 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 45 times 0, 1, 88 times 0, 1, 140 times 0, 1, 188 times 0) based on linear OA(1628, 514, F16, 14) (dual of [514, 486, 15]-code), using
- trace code [i] based on linear OA(25614, 257, F256, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using
- extended Reed–Solomon code RSe(243,256) [i]
- algebraic-geometric code AG(F,121P) 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 = 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+48P) with degQ = 2 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(1637, 1018, F16, 2, 14) (dual of [(1018, 2), 1999, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 37, 1018)-net over F16 | [i] | ||