Information on Result #1296994
Linear OA(1688, 654, F16, 39) (dual of [654, 566, 40]-code), using trace code based on linear OA(25644, 327, F256, 39) (dual of [327, 283, 40]-code), using
- construction X applied to AG(F,280P) ⊂ AG(F,284P) [i] based on
- linear OA(25641, 320, F256, 39) (dual of [320, 279, 40]-code), using algebraic-geometric code AG(F,280P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- linear OA(25637, 320, F256, 35) (dual of [320, 283, 36]-code), using algebraic-geometric code AG(F,284P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321 (see above)
- linear OA(2563, 7, F256, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,256) or 7-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
Mode: 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(1688, 645, F16, 2, 39) (dual of [(645, 2), 1202, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |