Information on Result #660889
Linear OA(9140, 752, F9, 51) (dual of [752, 612, 52]-code), using trace code based on linear OA(8170, 376, F81, 51) (dual of [376, 306, 52]-code), using
- construction X applied to AG(F,317P) ⊂ AG(F,321P) [i] based on
- linear OA(8167, 369, F81, 51) (dual of [369, 302, 52]-code), using algebraic-geometric code AG(F,317P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OA(8163, 369, F81, 47) (dual of [369, 306, 48]-code), using algebraic-geometric code AG(F,321P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OA(813, 7, F81, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,81) or 7-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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 OA(9141, 753, F9, 51) (dual of [753, 612, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9140, 376, F9, 2, 51) (dual of [(376, 2), 612, 52]-NRT-code) | [i] | OOA Folding | |