Information on Result #1044970
Linear OOA(972, 84, F9, 3, 40) (dual of [(84, 3), 180, 41]-NRT-code), using construction X applied to AG(3;F,190P) ⊂ AG(3;F,201P) based on
- linear OOA(962, 77, F9, 3, 40) (dual of [(77, 3), 169, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,190P) [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(951, 77, F9, 3, 29) (dual of [(77, 3), 180, 30]-NRT-code), using algebraic-geometric NRT-code AG(3;F,201P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78 (see above)
- linear OOA(910, 7, F9, 3, 10) (dual of [(7, 3), 11, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(910, 9, F9, 3, 10) (dual of [(9, 3), 17, 11]-NRT-code), using
- Reed–Solomon NRT-code RS(3;17,9) [i]
- discarding factors / shortening the dual code based on linear OOA(910, 9, F9, 3, 10) (dual of [(9, 3), 17, 11]-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(972, 84, F9, 3, 39) (dual of [(84, 3), 180, 40]-NRT-code) | [i] | Strength Reduction for OOAs | |