Information on Result #642761
Linear OA(4955, 59, F49, 52) (dual of [59, 4, 53]-code), using juxtaposition based on
- linear OA(495, 9, F49, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- linear OA(4946, 50, F49, 46) (dual of [50, 4, 47]-code or 50-arc in PG(45,49)), using
- extended Reed–Solomon code RSe(4,49) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- algebraic-geometric code AG(F,1P) with degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
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(4953, 57, F49, 50) (dual of [57, 4, 51]-code) | [i] | Truncation | |