Information on Result #657509
Linear OA(4930, 55, F49, 28) (dual of [55, 25, 29]-code), using construction X applied to AG(F,7P) ⊂ AG(F,8P) based on
- linear OA(4928, 50, F49, 28) (dual of [50, 22, 29]-code or 50-arc in PG(27,49)), using algebraic-geometric code AG(F, Q+9P) 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]
- linear OA(4925, 50, F49, 25) (dual of [50, 25, 26]-code or 50-arc in PG(24,49)), using algebraic-geometric code AG(F,12P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(492, 5, F49, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), 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(760, 110, F7, 28) (dual of [110, 50, 29]-code) | [i] | Trace Code | |
| 2 | Linear OA(4945, 108, F49, 28) (dual of [108, 63, 29]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4946, 110, F49, 28) (dual of [110, 64, 29]-code) | [i] | ||