Information on Result #655681
Linear OA(8173, 382, F81, 51) (dual of [382, 309, 52]-code), using construction X applied to AG(F,317P) ⊂ AG(F,324P) 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(8160, 369, F81, 44) (dual of [369, 309, 45]-code), using algebraic-geometric code AG(F,324P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OA(816, 13, F81, 6) (dual of [13, 7, 7]-code or 13-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), 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(9146, 764, F9, 51) (dual of [764, 618, 52]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8173, 191, F81, 2, 51) (dual of [(191, 2), 309, 52]-NRT-code) | [i] | OOA Folding | |