Information on Result #659829
Linear OA(5124, 264, F5, 49) (dual of [264, 140, 50]-code), using trace code based on linear OA(2562, 132, F25, 49) (dual of [132, 70, 50]-code), using
- construction X applied to AG(F,75P) ⊂ AG(F,79P) [i] based on
- linear OA(2559, 125, F25, 49) (dual of [125, 66, 50]-code), using algebraic-geometric code AG(F,75P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- linear OA(2555, 125, F25, 45) (dual of [125, 70, 46]-code), using algebraic-geometric code AG(F,79P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126 (see above)
- linear OA(253, 7, F25, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,25) or 7-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- linear OA(2559, 125, F25, 49) (dual of [125, 66, 50]-code), using algebraic-geometric code AG(F,75P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, 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(5125, 265, F5, 49) (dual of [265, 140, 50]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5124, 132, F5, 2, 49) (dual of [(132, 2), 140, 50]-NRT-code) | [i] | OOA Folding | |