Information on Result #659856
Linear OA(5130, 268, F5, 51) (dual of [268, 138, 52]-code), using trace code based on linear OA(2565, 134, F25, 51) (dual of [134, 69, 52]-code), using
- construction X applied to AG(F,73P) ⊂ AG(F,78P) [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(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(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(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(5131, 269, F5, 51) (dual of [269, 138, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5130, 134, F5, 2, 51) (dual of [(134, 2), 138, 52]-NRT-code) | [i] | OOA Folding | |