Information on Result #1044683
Linear OOA(989, 81, F9, 3, 61) (dual of [(81, 3), 154, 62]-NRT-code), using construction X applied to AG(3;F,169P) ⊂ AG(3;F,176P) based on
- linear OOA(983, 77, F9, 3, 61) (dual of [(77, 3), 148, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,169P) [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(976, 77, F9, 3, 54) (dual of [(77, 3), 155, 55]-NRT-code), using algebraic-geometric NRT-code AG(3;F,176P) [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(3178, 162, F3, 3, 61) (dual of [(162, 3), 308, 62]-NRT-code) | [i] | Trace Code for OOAs | |