Information on Result #1474813
Linear OOA(8169, 502, F81, 2, 40) (dual of [(502, 2), 935, 41]-NRT-code), using construction X applied to AG(2;F,957P) ⊂ AG(2;F,961P) based on
- linear OOA(8166, 499, F81, 2, 40) (dual of [(499, 2), 932, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,957P) [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
- linear OOA(8162, 499, F81, 2, 36) (dual of [(499, 2), 936, 37]-NRT-code), using algebraic-geometric NRT-code AG(2;F,961P) [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500 (see above)
- linear OOA(813, 3, F81, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(813, 81, F81, 2, 3) (dual of [(81, 2), 159, 4]-NRT-code), using
- Reed–Solomon NRT-code RS(2;159,81) [i]
- discarding factors / shortening the dual code based on linear OOA(813, 81, F81, 2, 3) (dual of [(81, 2), 159, 4]-NRT-code), using
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(8169, 502, F81, 3, 40) (dual of [(502, 3), 1437, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8169, 502, F81, 4, 40) (dual of [(502, 4), 1939, 41]-NRT-code) | [i] | ||
| 3 | Digital (29, 69, 502)-net over F81 | [i] | ||