Information on Result #654510
Linear OA(6480, 519, F64, 49) (dual of [519, 439, 50]-code), using construction X applied to AG(F,462P) ⊂ AG(F,466P) based on
- linear OA(6477, 512, F64, 49) (dual of [512, 435, 50]-code), using algebraic-geometric code AG(F,462P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- linear OA(6473, 512, F64, 45) (dual of [512, 439, 46]-code), using algebraic-geometric code AG(F,466P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513 (see above)
- linear OA(643, 7, F64, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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(8160, 1038, F8, 49) (dual of [1038, 878, 50]-code) | [i] | Trace Code | |
| 2 | Linear OOA(6480, 259, F64, 2, 49) (dual of [(259, 2), 438, 50]-NRT-code) | [i] | OOA Folding | |