Information on Result #646253
Linear OA(2563, 132, F25, 50) (dual of [132, 69, 51]-code), using construction X applied to AG(F,74P) ⊂ AG(F,78P) 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(2556, 125, F25, 46) (dual of [125, 69, 47]-code), using algebraic-geometric code AG(F,78P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126 (see above)
- linear OA(253, 7, F25, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,25) or 7-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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(5126, 264, F5, 50) (dual of [264, 138, 51]-code) | [i] | Trace Code | |
| 2 | Linear OOA(2563, 66, F25, 2, 50) (dual of [(66, 2), 69, 51]-NRT-code) | [i] | OOA Folding | |