Information on Result #657395
Linear OA(498, 50, F49, 8) (dual of [50, 42, 9]-code or 50-arc in PG(7,49)), using algebraic-geometric code AG(F, Q+19P) 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(716, 100, F7, 8) (dual of [100, 84, 9]-code) | [i] | Trace Code | |
| 2 | Linear OA(4926, 103, F49, 17) (dual of [103, 77, 18]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4941, 2452, F49, 17) (dual of [2452, 2411, 18]-code) | [i] | ||
| 4 | Linear OA(4924, 100, F49, 16) (dual of [100, 76, 17]-code) | [i] | ||
| 5 | Linear OA(4925, 103, F49, 16) (dual of [103, 78, 17]-code) | [i] | ||
| 6 | Linear OA(4939, 2451, F49, 16) (dual of [2451, 2412, 17]-code) | [i] | ||
| 7 | Linear OA(4954, 117699, F49, 16) (dual of [117699, 117645, 17]-code) | [i] | ||
| 8 | Linear OA(4912, 100, F49, 8) (dual of [100, 88, 9]-code) | [i] | ||
| 9 | Linear OA(4941, 2453, F49, 17) (dual of [2453, 2412, 18]-code) | [i] | ||
| 10 | Linear OA(4942, 2457, F49, 17) (dual of [2457, 2415, 18]-code) | [i] | ||
| 11 | Linear OA(4944, 2463, F49, 17) (dual of [2463, 2419, 18]-code) | [i] | ||
| 12 | Linear OA(4939, 2453, F49, 16) (dual of [2453, 2414, 17]-code) | [i] | ||
| 13 | Linear OA(4954, 117702, F49, 16) (dual of [117702, 117648, 17]-code) | [i] | ||
| 14 | Linear OA(4955, 117706, F49, 16) (dual of [117706, 117651, 17]-code) | [i] | ||
| 15 | Linear OA(4926, 114, F49, 17) (dual of [114, 88, 18]-code) | [i] | ||
| 16 | Linear OA(4925, 114, F49, 16) (dual of [114, 89, 17]-code) | [i] | ||
| 17 | Linear OA(4920, 2450, F49, 8) (dual of [2450, 2430, 9]-code) | [i] | Generalized (u, u+v)-Construction | |
| 18 | Linear OA(4911, 53, F49, 10) (dual of [53, 42, 11]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 19 | Linear OA(499, 53, F49, 8) (dual of [53, 44, 9]-code) | [i] | ✔ | |
| 20 | Linear OA(4915, 57, F49, 12) (dual of [57, 42, 13]-code) | [i] | ✔ | |
| 21 | Linear OA(4911, 57, F49, 8) (dual of [57, 46, 9]-code) | [i] | ✔ | |
| 22 | Linear OA(4919, 61, F49, 14) (dual of [61, 42, 15]-code) | [i] | ✔ | |
| 23 | Linear OA(4923, 65, F49, 16) (dual of [65, 42, 17]-code) | [i] | ✔ | |
| 24 | Linear OA(4913, 55, F49, 11) (dual of [55, 42, 12]-code) | [i] | ✔ | |
| 25 | Linear OA(4910, 55, F49, 8) (dual of [55, 45, 9]-code) | [i] | ✔ | |
| 26 | Linear OA(4917, 59, F49, 13) (dual of [59, 42, 14]-code) | [i] | ✔ | |
| 27 | Linear OA(4946, 2502, F49, 17) (dual of [2502, 2456, 18]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 28 | Linear OA(4944, 2501, F49, 16) (dual of [2501, 2457, 17]-code) | [i] | ||