Information on Result #628271
Linear OA(728, 100, F7, 14) (dual of [100, 72, 15]-code), using trace code based on linear OA(4914, 50, F49, 14) (dual of [50, 36, 15]-code or 50-arc in PG(13,49)), using
- extended Reed–Solomon code RSe(36,49) [i]
- algebraic-geometric code AG(F, Q+16P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- algebraic-geometric code AG(F, Q+11P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F,7P) with degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(729, 101, F7, 14) (dual of [101, 72, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(728, 50, F7, 2, 14) (dual of [(50, 2), 72, 15]-NRT-code) | [i] | OOA Folding | |