Information on Result #657393
Linear OA(4910, 50, F49, 10) (dual of [50, 40, 11]-code or 50-arc in PG(9,49)), using algebraic-geometric code AG(F, Q+18P) with degQ = 3 and degPÂ =Â 2 based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
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
- Extended Reed–Solomon Code [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(720, 100, F7, 10) (dual of [100, 80, 11]-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(4951, 2452, F49, 21) (dual of [2452, 2401, 22]-code) | [i] | ||
| 4 | Linear OA(4930, 100, F49, 20) (dual of [100, 70, 21]-code) | [i] | ||
| 5 | Linear OA(4931, 103, F49, 20) (dual of [103, 72, 21]-code) | [i] | ||
| 6 | Linear OA(4949, 2451, F49, 20) (dual of [2451, 2402, 21]-code) | [i] | ||
| 7 | Linear OA(4951, 2453, F49, 21) (dual of [2453, 2402, 22]-code) | [i] | ||
| 8 | Linear OA(4952, 2457, F49, 21) (dual of [2457, 2405, 22]-code) | [i] | ||
| 9 | Linear OA(4954, 2463, F49, 21) (dual of [2463, 2409, 22]-code) | [i] | ||
| 10 | Linear OA(4949, 2453, F49, 20) (dual of [2453, 2404, 21]-code) | [i] | ||
| 11 | Linear OA(4932, 114, F49, 21) (dual of [114, 82, 22]-code) | [i] | ||
| 12 | Linear OA(4931, 114, F49, 20) (dual of [114, 83, 21]-code) | [i] | ||
| 13 | Linear OA(4913, 53, F49, 12) (dual of [53, 40, 13]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 14 | Linear OA(4911, 53, F49, 10) (dual of [53, 42, 11]-code) | [i] | ✔ | |
| 15 | Linear OA(4917, 57, F49, 14) (dual of [57, 40, 15]-code) | [i] | ✔ | |
| 16 | Linear OA(4913, 57, F49, 10) (dual of [57, 44, 11]-code) | [i] | ✔ | |
| 17 | Linear OA(4921, 61, F49, 16) (dual of [61, 40, 17]-code) | [i] | ✔ | |
| 18 | Linear OA(4925, 65, F49, 18) (dual of [65, 40, 19]-code) | [i] | ✔ | |
| 19 | Linear OA(4929, 69, F49, 20) (dual of [69, 40, 21]-code) | [i] | ✔ | |
| 20 | Linear OA(4915, 55, F49, 13) (dual of [55, 40, 14]-code) | [i] | ✔ | |
| 21 | Linear OA(4912, 55, F49, 10) (dual of [55, 43, 11]-code) | [i] | ✔ | |
| 22 | Linear OA(4927, 67, F49, 19) (dual of [67, 40, 20]-code) | [i] | ✔ | |
| 23 | Linear OA(4919, 59, F49, 15) (dual of [59, 40, 16]-code) | [i] | ✔ | |
| 24 | Linear OA(4914, 59, F49, 10) (dual of [59, 45, 11]-code) | [i] | ✔ | |
| 25 | Linear OA(4955, 2501, F49, 20) (dual of [2501, 2446, 21]-code) | [i] | (u, u−v, u+v+w)-Construction | |