Information on Result #657383
Linear OA(4920, 50, F49, 20) (dual of [50, 30, 21]-code or 50-arc in PG(19,49)), using algebraic-geometric code AG(F, Q+13P) 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(740, 100, F7, 20) (dual of [100, 60, 21]-code) | [i] | Trace Code | |
| 2 | Linear OA(4930, 100, F49, 20) (dual of [100, 70, 21]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(790, 150, F7, 41) (dual of [150, 60, 42]-code) | [i] | Concatenation of Two Codes | |
| 4 | Linear OA(4923, 53, F49, 22) (dual of [53, 30, 23]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 5 | Linear OA(4921, 53, F49, 20) (dual of [53, 32, 21]-code) | [i] | ✔ | |
| 6 | Linear OA(4927, 57, F49, 24) (dual of [57, 30, 25]-code) | [i] | ✔ | |
| 7 | Linear OA(4923, 57, F49, 20) (dual of [57, 34, 21]-code) | [i] | ✔ | |
| 8 | Linear OA(4931, 61, F49, 26) (dual of [61, 30, 27]-code) | [i] | ✔ | |
| 9 | Linear OA(4925, 61, F49, 20) (dual of [61, 36, 21]-code) | [i] | ✔ | |
| 10 | Linear OA(4935, 65, F49, 28) (dual of [65, 30, 29]-code) | [i] | ✔ | |
| 11 | Linear OA(4927, 65, F49, 20) (dual of [65, 38, 21]-code) | [i] | ✔ | |
| 12 | Linear OA(4939, 69, F49, 30) (dual of [69, 30, 31]-code) | [i] | ✔ | |
| 13 | Linear OA(4929, 69, F49, 20) (dual of [69, 40, 21]-code) | [i] | ✔ | |
| 14 | Linear OA(4943, 73, F49, 32) (dual of [73, 30, 33]-code) | [i] | ✔ | |
| 15 | Linear OA(4947, 77, F49, 34) (dual of [77, 30, 35]-code) | [i] | ✔ | |
| 16 | Linear OA(4951, 81, F49, 36) (dual of [81, 30, 37]-code) | [i] | ✔ | |
| 17 | Linear OA(4925, 55, F49, 23) (dual of [55, 30, 24]-code) | [i] | ✔ | |
| 18 | Linear OA(4922, 55, F49, 20) (dual of [55, 33, 21]-code) | [i] | ✔ | |
| 19 | Linear OA(4937, 67, F49, 29) (dual of [67, 30, 30]-code) | [i] | ✔ | |
| 20 | Linear OA(4928, 67, F49, 20) (dual of [67, 39, 21]-code) | [i] | ✔ | |
| 21 | Linear OA(4949, 79, F49, 35) (dual of [79, 30, 36]-code) | [i] | ✔ | |
| 22 | Linear OA(4929, 59, F49, 25) (dual of [59, 30, 26]-code) | [i] | ✔ | |
| 23 | Linear OA(4924, 59, F49, 20) (dual of [59, 35, 21]-code) | [i] | ✔ | |