Information on Result #1048152
Linear OOA(3206, 172, F3, 3, 68) (dual of [(172, 3), 310, 69]-NRT-code), using trace code based on linear OOA(9103, 86, F9, 3, 68) (dual of [(86, 3), 155, 69]-NRT-code), using
- construction X applied to AG(3;F,162P) ⊂ AG(3;F,176P) [i] based on
- linear OOA(990, 77, F9, 3, 68) (dual of [(77, 3), 141, 69]-NRT-code), using algebraic-geometric NRT-code AG(3;F,162P) [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(913, 9, F9, 3, 13) (dual of [(9, 3), 14, 14]-NRT-code), using
- Reed–Solomon NRT-code RS(3;14,9) [i]
- linear OOA(990, 77, F9, 3, 68) (dual of [(77, 3), 141, 69]-NRT-code), using algebraic-geometric NRT-code AG(3;F,162P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, 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(3206, 172, F3, 3, 67) (dual of [(172, 3), 310, 68]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3209, 173, F3, 3, 68) (dual of [(173, 3), 310, 69]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(3207, 172, F3, 3, 68) (dual of [(172, 3), 309, 69]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(3206, 86, F3, 5, 68) (dual of [(86, 5), 224, 69]-NRT-code) | [i] | OOA Folding | |