Information on Result #1049002
Linear OOA(9144, 744, F9, 3, 52) (dual of [(744, 3), 2088, 53]-NRT-code), using trace code based on linear OOA(8172, 372, F81, 3, 52) (dual of [(372, 3), 1044, 53]-NRT-code), using
- construction X applied to AG(3;F,1054P) ⊂ AG(3;F,1059P) [i] based on
- linear OOA(8168, 369, F81, 3, 52) (dual of [(369, 3), 1039, 53]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1054P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OOA(8163, 369, F81, 3, 47) (dual of [(369, 3), 1044, 48]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1059P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OOA(814, 3, F81, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 81, F81, 3, 4) (dual of [(81, 3), 239, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(3;239,81) [i]
- discarding factors / shortening the dual code based on linear OOA(814, 81, F81, 3, 4) (dual of [(81, 3), 239, 5]-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(9144, 744, F9, 3, 51) (dual of [(744, 3), 2088, 52]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(9147, 745, F9, 3, 52) (dual of [(745, 3), 2088, 53]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(9145, 744, F9, 3, 52) (dual of [(744, 3), 2087, 53]-NRT-code) | [i] | OOA Duplication | |