Information on Result #1311441
Linear OA(713, 103, F7, 6) (dual of [103, 90, 7]-code), using 2 step Varšamov–Edel lengthening with (ri) = (1, 0) based on linear OA(712, 100, F7, 6) (dual of [100, 88, 7]-code), using
- trace code [i] based on linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using
- extended Reed–Solomon code RSe(44,49) [i]
- algebraic-geometric code AG(F, Q+20P) 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+13P) with degQ = 4 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, Q+8P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (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(713, 103, F7, 2, 6) (dual of [(103, 2), 193, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(713, 103, F7, 3, 6) (dual of [(103, 3), 296, 7]-NRT-code) | [i] | ||
| 3 | Digital (7, 13, 103)-net over F7 | [i] | ||