Information on Result #659893
Linear OA(5138, 284, F5, 51) (dual of [284, 146, 52]-code), using trace code based on linear OA(2569, 142, F25, 51) (dual of [142, 73, 52]-code), using
- construction X applied to AG(F,73P) ⊂ AG(F,82P) [i] based on
- linear OA(2561, 125, F25, 51) (dual of [125, 64, 52]-code), using algebraic-geometric code AG(F,73P) [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(258, 17, F25, 8) (dual of [17, 9, 9]-code or 17-arc in PG(7,25)), using
- discarding factors / shortening the dual code based on linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- Reed–Solomon code RS(17,25) [i]
- discarding factors / shortening the dual code based on linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- linear OA(2561, 125, F25, 51) (dual of [125, 64, 52]-code), using algebraic-geometric code AG(F,73P) [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(5139, 285, F5, 51) (dual of [285, 146, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5138, 142, F5, 2, 51) (dual of [(142, 2), 146, 52]-NRT-code) | [i] | OOA Folding | |