Information on Result #655132
Linear OA(8166, 178, F81, 56) (dual of [178, 112, 57]-code), using construction X applied to AG(F,114P) ⊂ AG(F,118P) based on
- linear OA(8163, 171, F81, 56) (dual of [171, 108, 57]-code), using algebraic-geometric code AG(F,114P) [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- linear OA(8159, 171, F81, 52) (dual of [171, 112, 53]-code), using algebraic-geometric code AG(F,118P) [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172 (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(9132, 356, F9, 56) (dual of [356, 224, 57]-code) | [i] | Trace Code | |
| 2 | OA(2788, 178, S27, 56) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8166, 89, F81, 2, 56) (dual of [(89, 2), 112, 57]-NRT-code) | [i] | OOA Folding | |