Information on Result #659873
Linear OA(5134, 280, F5, 50) (dual of [280, 146, 51]-code), using trace code based on linear OA(2567, 140, F25, 50) (dual of [140, 73, 51]-code), using
- construction X applied to AG(F,74P) ⊂ AG(F,82P) [i] based on
- linear OA(2560, 125, F25, 50) (dual of [125, 65, 51]-code), using algebraic-geometric code AG(F,74P) [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(2552, 125, F25, 42) (dual of [125, 73, 43]-code), using algebraic-geometric code AG(F,82P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126 (see above)
- linear OA(257, 15, F25, 7) (dual of [15, 8, 8]-code or 15-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- linear OA(2560, 125, F25, 50) (dual of [125, 65, 51]-code), using algebraic-geometric code AG(F,74P) [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(5135, 281, F5, 50) (dual of [281, 146, 51]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5134, 140, F5, 2, 50) (dual of [(140, 2), 146, 51]-NRT-code) | [i] | OOA Folding | |