Information on Result #1048953
Linear OOA(9128, 748, F9, 3, 41) (dual of [(748, 3), 2116, 42]-NRT-code), using trace code based on linear OOA(8164, 374, F81, 3, 41) (dual of [(374, 3), 1058, 42]-NRT-code), using
- construction X applied to AG(3;F,1065P) ⊂ AG(3;F,1073P) [i] based on
- linear OOA(8157, 369, F81, 3, 41) (dual of [(369, 3), 1050, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1065P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OOA(8149, 369, F81, 3, 33) (dual of [(369, 3), 1058, 34]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1073P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OOA(817, 5, F81, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(817, 81, F81, 3, 7) (dual of [(81, 3), 236, 8]-NRT-code), using
- Reed–Solomon NRT-code RS(3;236,81) [i]
- discarding factors / shortening the dual code based on linear OOA(817, 81, F81, 3, 7) (dual of [(81, 3), 236, 8]-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(9128, 748, F9, 3, 40) (dual of [(748, 3), 2116, 41]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(9131, 749, F9, 3, 41) (dual of [(749, 3), 2116, 42]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(9129, 748, F9, 3, 41) (dual of [(748, 3), 2115, 42]-NRT-code) | [i] | OOA Duplication | |