Information on Result #1048170
Linear OOA(3210, 172, F3, 3, 70) (dual of [(172, 3), 306, 71]-NRT-code), using trace code based on linear OOA(9105, 86, F9, 3, 70) (dual of [(86, 3), 153, 71]-NRT-code), using
- construction X applied to AG(3;F,160P) ⊂ AG(3;F,174P) [i] based on
- linear OOA(992, 77, F9, 3, 70) (dual of [(77, 3), 139, 71]-NRT-code), using algebraic-geometric NRT-code AG(3;F,160P) [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(978, 77, F9, 3, 56) (dual of [(77, 3), 153, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,174P) [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(992, 77, F9, 3, 70) (dual of [(77, 3), 139, 71]-NRT-code), using algebraic-geometric NRT-code AG(3;F,160P) [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(3210, 172, F3, 3, 69) (dual of [(172, 3), 306, 70]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3213, 173, F3, 3, 70) (dual of [(173, 3), 306, 71]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(3211, 172, F3, 3, 70) (dual of [(172, 3), 305, 71]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(3210, 86, F3, 5, 70) (dual of [(86, 5), 220, 71]-NRT-code) | [i] | OOA Folding | |