Information on Result #1044783
Linear OOA(982, 82, F9, 3, 53) (dual of [(82, 3), 164, 54]-NRT-code), using construction X applied to AG(3;F,177P) ⊂ AG(3;F,185P) based on
- linear OOA(975, 77, F9, 3, 53) (dual of [(77, 3), 156, 54]-NRT-code), using algebraic-geometric NRT-code AG(3;F,177P) [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(967, 77, F9, 3, 45) (dual of [(77, 3), 164, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,185P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78 (see above)
- linear OOA(97, 5, F9, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(97, 9, F9, 3, 7) (dual of [(9, 3), 20, 8]-NRT-code), using
- Reed–Solomon NRT-code RS(3;20,9) [i]
- discarding factors / shortening the dual code based on linear OOA(97, 9, F9, 3, 7) (dual of [(9, 3), 20, 8]-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(3164, 164, F3, 3, 53) (dual of [(164, 3), 328, 54]-NRT-code) | [i] | Trace Code for OOAs | |