Information on Result #1045033
Linear OOA(992, 85, F9, 3, 58) (dual of [(85, 3), 163, 59]-NRT-code), using construction X applied to AG(3;F,172P) ⊂ AG(3;F,185P) based on
- linear OOA(980, 77, F9, 3, 58) (dual of [(77, 3), 151, 59]-NRT-code), using algebraic-geometric NRT-code AG(3;F,172P) [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(912, 8, F9, 3, 12) (dual of [(8, 3), 12, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(912, 9, F9, 3, 12) (dual of [(9, 3), 15, 13]-NRT-code), using
- Reed–Solomon NRT-code RS(3;15,9) [i]
- discarding factors / shortening the dual code based on linear OOA(912, 9, F9, 3, 12) (dual of [(9, 3), 15, 13]-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(3184, 170, F3, 3, 58) (dual of [(170, 3), 326, 59]-NRT-code) | [i] | Trace Code for OOAs | |