Information on Result #657260
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 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]
- Expurgated Narrow-Sense BCH-Codes (BCH-Bound) [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(718, 100, F7, 9) (dual of [100, 82, 10]-code) | [i] | Trace Code | |
| 2 | Linear OA(4928, 100, F49, 19) (dual of [100, 72, 20]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4929, 103, F49, 19) (dual of [103, 74, 20]-code) | [i] | ||
| 4 | Linear OA(4946, 2452, F49, 19) (dual of [2452, 2406, 20]-code) | [i] | ||
| 5 | Linear OA(4928, 103, F49, 18) (dual of [103, 75, 19]-code) | [i] | ||
| 6 | Linear OA(4944, 2451, F49, 18) (dual of [2451, 2407, 19]-code) | [i] | ||
| 7 | Linear OA(4946, 2453, F49, 19) (dual of [2453, 2407, 20]-code) | [i] | ||
| 8 | Linear OA(4947, 2457, F49, 19) (dual of [2457, 2410, 20]-code) | [i] | ||
| 9 | Linear OA(4949, 2463, F49, 19) (dual of [2463, 2414, 20]-code) | [i] | ||
| 10 | Linear OA(4944, 2453, F49, 18) (dual of [2453, 2409, 19]-code) | [i] | ||
| 11 | Linear OA(4929, 114, F49, 19) (dual of [114, 85, 20]-code) | [i] | ||
| 12 | Linear OA(4928, 114, F49, 18) (dual of [114, 86, 19]-code) | [i] | ||
| 13 | Linear OA(4923, 2450, F49, 9) (dual of [2450, 2427, 10]-code) | [i] | Generalized (u, u+v)-Construction | |
| 14 | Linear OA(4912, 53, F49, 11) (dual of [53, 41, 12]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 15 | Linear OA(4910, 53, F49, 9) (dual of [53, 43, 10]-code) | [i] | ✔ | |
| 16 | Linear OA(4916, 57, F49, 13) (dual of [57, 41, 14]-code) | [i] | ✔ | |
| 17 | Linear OA(4912, 57, F49, 9) (dual of [57, 45, 10]-code) | [i] | ✔ | |
| 18 | Linear OA(4920, 61, F49, 15) (dual of [61, 41, 16]-code) | [i] | ✔ | |
| 19 | Linear OA(4924, 65, F49, 17) (dual of [65, 41, 18]-code) | [i] | ✔ | |
| 20 | Linear OA(4914, 55, F49, 12) (dual of [55, 41, 13]-code) | [i] | ✔ | |
| 21 | Linear OA(4911, 55, F49, 9) (dual of [55, 44, 10]-code) | [i] | ✔ | |
| 22 | Linear OA(4926, 67, F49, 18) (dual of [67, 41, 19]-code) | [i] | ✔ | |
| 23 | Linear OA(4918, 59, F49, 14) (dual of [59, 41, 15]-code) | [i] | ✔ | |
| 24 | Linear OA(4952, 2502, F49, 19) (dual of [2502, 2450, 20]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 25 | Linear OA(4950, 2501, F49, 18) (dual of [2501, 2451, 19]-code) | [i] | ||