Information on Result #657259
Linear OA(4912, 53, F49, 11) (dual of [53, 41, 12]-code), using construction X applied to AG(F,19P) ⊂ AG(F,20P) based on
- linear OA(4911, 50, F49, 11) (dual of [50, 39, 12]-code or 50-arc in PG(10,49)), using algebraic-geometric code AG(F,19P) 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(499, 50, F49, 9) (dual of [50, 41, 10]-code or 50-arc in PG(8,49)), using algebraic-geometric code AG(F,20P) 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(724, 106, F7, 11) (dual of [106, 82, 12]-code) | [i] | Trace Code | |
| 2 | Linear OA(4936, 106, F49, 23) (dual of [106, 70, 24]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4937, 108, F49, 23) (dual of [108, 71, 24]-code) | [i] | ||
| 4 | Linear OA(4935, 106, F49, 22) (dual of [106, 71, 23]-code) | [i] | ||
| 5 | Linear OA(4936, 108, F49, 22) (dual of [108, 72, 23]-code) | [i] | ||
| 6 | Linear OA(4955, 2454, F49, 22) (dual of [2454, 2399, 23]-code) | [i] | ||
| 7 | Linear OA(4917, 103, F49, 11) (dual of [103, 86, 12]-code) | [i] | ||
| 8 | Linear OA(4918, 106, F49, 11) (dual of [106, 88, 12]-code) | [i] | ||
| 9 | Linear OA(4955, 2456, F49, 22) (dual of [2456, 2401, 23]-code) | [i] | ||