Information on Result #655123
Linear OA(8175, 178, F81, 65) (dual of [178, 103, 66]-code), using construction X applied to AG(F,105P) ⊂ AG(F,109P) based on
- linear OA(8172, 171, F81, 65) (dual of [171, 99, 66]-code), using algebraic-geometric code AG(F,105P) [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- linear OA(8168, 171, F81, 61) (dual of [171, 103, 62]-code), using algebraic-geometric code AG(F,109P) [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(9150, 356, F9, 65) (dual of [356, 206, 66]-code) | [i] | Trace Code | |
| 2 | OA(27100, 178, S27, 65) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8175, 89, F81, 2, 65) (dual of [(89, 2), 103, 66]-NRT-code) | [i] | OOA Folding | |