Information on Result #1474781
Linear OOA(8137, 300, F81, 2, 22) (dual of [(300, 2), 563, 23]-NRT-code), using construction X applied to AG(2;F,571P) ⊂ AG(2;F,575P) based on
- linear OOA(8134, 297, F81, 2, 22) (dual of [(297, 2), 560, 23]-NRT-code), using algebraic-geometric NRT-code AG(2;F,571P) [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- linear OOA(8130, 297, F81, 2, 18) (dual of [(297, 2), 564, 19]-NRT-code), using algebraic-geometric NRT-code AG(2;F,575P) [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298 (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(8137, 300, F81, 3, 22) (dual of [(300, 3), 863, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8137, 300, F81, 4, 22) (dual of [(300, 4), 1163, 23]-NRT-code) | [i] | ||
| 3 | Digital (15, 37, 300)-net over F81 | [i] | ||