Information on Result #657263
Linear OA(498, 53, F49, 7) (dual of [53, 45, 8]-code), using construction X applied to AG(F,21P) ⊂ AG(F,22P) 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(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using algebraic-geometric code AG(F,22P) 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(716, 106, F7, 7) (dual of [106, 90, 8]-code) | [i] | Trace Code | |
| 2 | Linear OA(4924, 106, F49, 15) (dual of [106, 82, 16]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4937, 2455, F49, 15) (dual of [2455, 2418, 16]-code) | [i] | ||
| 4 | Linear OA(4951, 117703, F49, 15) (dual of [117703, 117652, 16]-code) | [i] | ||
| 5 | Linear OA(4935, 2454, F49, 14) (dual of [2454, 2419, 15]-code) | [i] | ||
| 6 | Linear OA(4948, 117702, F49, 14) (dual of [117702, 117654, 15]-code) | [i] | ||
| 7 | Linear OA(4937, 2456, F49, 15) (dual of [2456, 2419, 16]-code) | [i] | ||
| 8 | Linear OA(4938, 2460, F49, 15) (dual of [2460, 2422, 16]-code) | [i] | ||
| 9 | Linear OA(4951, 117705, F49, 15) (dual of [117705, 117654, 16]-code) | [i] | ||
| 10 | Linear OA(4952, 117710, F49, 15) (dual of [117710, 117658, 16]-code) | [i] | ||
| 11 | Linear OA(4935, 2456, F49, 14) (dual of [2456, 2421, 15]-code) | [i] | ||
| 12 | Linear OA(4936, 2459, F49, 14) (dual of [2459, 2423, 15]-code) | [i] | ||
| 13 | Linear OA(4948, 117705, F49, 14) (dual of [117705, 117657, 15]-code) | [i] | ||
| 14 | Linear OA(4949, 117709, F49, 14) (dual of [117709, 117660, 15]-code) | [i] | ||
| 15 | Linear OA(4917, 2453, F49, 7) (dual of [2453, 2436, 8]-code) | [i] | Generalized (u, u+v)-Construction | |
| 16 | Linear OA(4952, 117752, F49, 14) (dual of [117752, 117700, 15]-code) | [i] | (u, u−v, u+v+w)-Construction | |