Information on Result #659858
Linear OA(5130, 260, F5, 53) (dual of [260, 130, 54]-code), using trace code based on linear OA(2565, 130, F25, 53) (dual of [130, 65, 54]-code), using
- construction X applied to AG(F,71P) ⊂ AG(F,74P) [i] based on
- linear OA(2563, 125, F25, 53) (dual of [125, 62, 54]-code), using algebraic-geometric code AG(F,71P) [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(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 (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(2563, 125, F25, 53) (dual of [125, 62, 54]-code), using algebraic-geometric code AG(F,71P) [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(5131, 261, F5, 53) (dual of [261, 130, 54]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5130, 130, F5, 2, 53) (dual of [(130, 2), 130, 54]-NRT-code) | [i] | OOA Folding | |