Information on Result #1044678
Linear OOA(994, 81, F9, 3, 66) (dual of [(81, 3), 149, 67]-NRT-code), using construction X applied to AG(3;F,164P) ⊂ AG(3;F,171P) based on
- linear OOA(988, 77, F9, 3, 66) (dual of [(77, 3), 143, 67]-NRT-code), using algebraic-geometric NRT-code AG(3;F,164P) [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(981, 77, F9, 3, 59) (dual of [(77, 3), 150, 60]-NRT-code), using algebraic-geometric NRT-code AG(3;F,171P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78 (see above)
- linear OOA(96, 4, F9, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(96, 9, F9, 3, 6) (dual of [(9, 3), 21, 7]-NRT-code), using
- Reed–Solomon NRT-code RS(3;21,9) [i]
- discarding factors / shortening the dual code based on linear OOA(96, 9, F9, 3, 6) (dual of [(9, 3), 21, 7]-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(3188, 162, F3, 3, 66) (dual of [(162, 3), 298, 67]-NRT-code) | [i] | Trace Code for OOAs | |