Information on Result #659806
Linear OA(5118, 260, F5, 47) (dual of [260, 142, 48]-code), using trace code based on linear OA(2559, 130, F25, 47) (dual of [130, 71, 48]-code), using
- construction X applied to AG(F,77P) ⊂ AG(F,80P) [i] based on
- linear OA(2557, 125, F25, 47) (dual of [125, 68, 48]-code), using algebraic-geometric code AG(F,77P) [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(2554, 125, F25, 44) (dual of [125, 71, 45]-code), using algebraic-geometric code AG(F,80P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- linear OA(2557, 125, F25, 47) (dual of [125, 68, 48]-code), using algebraic-geometric code AG(F,77P) [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(5119, 261, F5, 47) (dual of [261, 142, 48]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5118, 130, F5, 2, 47) (dual of [(130, 2), 142, 48]-NRT-code) | [i] | OOA Folding | |