Information on Result #659746
Linear OA(5102, 268, F5, 37) (dual of [268, 166, 38]-code), using trace code based on linear OA(2551, 134, F25, 37) (dual of [134, 83, 38]-code), using
- construction X applied to AG(F,87P) ⊂ AG(F,92P) [i] based on
- linear OA(2547, 125, F25, 37) (dual of [125, 78, 38]-code), using algebraic-geometric code AG(F,87P) [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(2542, 125, F25, 32) (dual of [125, 83, 33]-code), using algebraic-geometric code AG(F,92P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126 (see above)
- linear OA(254, 9, F25, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- linear OA(2547, 125, F25, 37) (dual of [125, 78, 38]-code), using algebraic-geometric code AG(F,87P) [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(5103, 269, F5, 37) (dual of [269, 166, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5102, 134, F5, 2, 37) (dual of [(134, 2), 166, 38]-NRT-code) | [i] | OOA Folding | |