Information on Result #1044578
Linear OOA(975, 80, F9, 3, 49) (dual of [(80, 3), 165, 50]-NRT-code), using construction X applied to AG(3;F,181P) ⊂ AG(3;F,186P) based on
- linear OOA(971, 77, F9, 3, 49) (dual of [(77, 3), 160, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,181P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- linear OOA(966, 77, F9, 3, 44) (dual of [(77, 3), 165, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,186P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78 (see above)
- linear OOA(94, 3, F9, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(94, 9, F9, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(3;23,9) [i]
- discarding factors / shortening the dual code based on linear OOA(94, 9, F9, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3150, 160, F3, 3, 49) (dual of [(160, 3), 330, 50]-NRT-code) | [i] | Trace Code for OOAs | |