Information on Result #657249
Linear OA(4922, 53, F49, 21) (dual of [53, 31, 22]-code), using construction X applied to AG(F,14P) ⊂ AG(F,15P) based on
- linear OA(4921, 50, F49, 21) (dual of [50, 29, 22]-code or 50-arc in PG(20,49)), using algebraic-geometric code AG(F,14P) with 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]
- linear OA(4919, 50, F49, 19) (dual of [50, 31, 20]-code or 50-arc in PG(18,49)), using algebraic-geometric code AG(F,15P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(491, 3, F49, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(744, 106, F7, 21) (dual of [106, 62, 22]-code) | [i] | Trace Code | |
| 2 | Linear OA(4932, 103, F49, 21) (dual of [103, 71, 22]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4933, 106, F49, 21) (dual of [106, 73, 22]-code) | [i] | ||