Information on Result #659823
Linear OA(5122, 256, F5, 50) (dual of [256, 134, 51]-code), using trace code based on linear OA(2561, 128, F25, 50) (dual of [128, 67, 51]-code), using
- construction X applied to AG(F,74P) ⊂ AG(F,76P) [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(2558, 125, F25, 48) (dual of [125, 67, 49]-code), using algebraic-geometric code AG(F,76P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(5123, 257, F5, 50) (dual of [257, 134, 51]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5122, 128, F5, 2, 50) (dual of [(128, 2), 134, 51]-NRT-code) | [i] | OOA Folding | |