Information on Result #655598
Linear OA(8145, 376, F81, 26) (dual of [376, 331, 27]-code), using construction X applied to AG(F,342P) ⊂ AG(F,346P) based on
- linear OA(8142, 369, F81, 26) (dual of [369, 327, 27]-code), using algebraic-geometric code AG(F,342P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OA(8138, 369, F81, 22) (dual of [369, 331, 23]-code), using algebraic-geometric code AG(F,346P) [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 OOA(8145, 376, F81, 2, 26) (dual of [(376, 2), 707, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8145, 376, F81, 3, 26) (dual of [(376, 3), 1083, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(8145, 376, F81, 4, 26) (dual of [(376, 4), 1459, 27]-NRT-code) | [i] | ||
| 4 | Digital (19, 45, 376)-net over F81 | [i] | ||
| 5 | Linear OOA(8145, 188, F81, 2, 26) (dual of [(188, 2), 331, 27]-NRT-code) | [i] | OOA Folding | |