Information on Result #657523
Linear OA(499, 55, F49, 7) (dual of [55, 46, 8]-code), using construction X applied to AG(F,14P) ⊂ AG(F,15P) based on
- linear OA(497, 50, F49, 7) (dual of [50, 43, 8]-code or 50-arc in PG(6,49)), using algebraic-geometric code AG(F,21P) 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(494, 50, F49, 4) (dual of [50, 46, 5]-code or 50-arc in PG(3,49)), using algebraic-geometric code AG(F, Q+21P) with degQ = 3 and 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(4938, 2457, F49, 15) (dual of [2457, 2419, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(4952, 117705, F49, 15) (dual of [117705, 117653, 16]-code) | [i] | ||
| 3 | Linear OA(4936, 2456, F49, 14) (dual of [2456, 2420, 15]-code) | [i] | ||
| 4 | Linear OA(4949, 117704, F49, 14) (dual of [117704, 117655, 15]-code) | [i] | ||
| 5 | Linear OA(4938, 2458, F49, 15) (dual of [2458, 2420, 16]-code) | [i] | ||
| 6 | Linear OA(4952, 117707, F49, 15) (dual of [117707, 117655, 16]-code) | [i] | ||
| 7 | Linear OA(4936, 2458, F49, 14) (dual of [2458, 2422, 15]-code) | [i] | ||
| 8 | Linear OA(4949, 117707, F49, 14) (dual of [117707, 117658, 15]-code) | [i] | ||