Information on Result #659885
Linear OA(5136, 272, F5, 53) (dual of [272, 136, 54]-code), using trace code based on linear OA(2568, 136, F25, 53) (dual of [136, 68, 54]-code), using
- construction X applied to AG(F,71P) ⊂ AG(F,77P) [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(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 (see above)
- linear OA(255, 11, F25, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), 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(5137, 273, F5, 53) (dual of [273, 136, 54]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5136, 136, F5, 2, 53) (dual of [(136, 2), 136, 54]-NRT-code) | [i] | OOA Folding | |