Information on Result #657375
Linear OA(4928, 50, F49, 28) (dual of [50, 22, 29]-code or 50-arc in PG(27,49)), using algebraic-geometric code AG(F, Q+9P) 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(756, 100, F7, 28) (dual of [100, 44, 29]-code) | [i] | Trace Code | |
| 2 | Linear OA(4942, 100, F49, 28) (dual of [100, 58, 29]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(7106, 150, F7, 57) (dual of [150, 44, 58]-code) | [i] | Concatenation of Two Codes | |
| 4 | Linear OA(4931, 53, F49, 30) (dual of [53, 22, 31]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 5 | Linear OA(4929, 53, F49, 28) (dual of [53, 24, 29]-code) | [i] | ✔ | |
| 6 | Linear OA(4935, 57, F49, 32) (dual of [57, 22, 33]-code) | [i] | ✔ | |
| 7 | Linear OA(4931, 57, F49, 28) (dual of [57, 26, 29]-code) | [i] | ✔ | |
| 8 | Linear OA(4939, 61, F49, 34) (dual of [61, 22, 35]-code) | [i] | ✔ | |
| 9 | Linear OA(4933, 61, F49, 28) (dual of [61, 28, 29]-code) | [i] | ✔ | |
| 10 | Linear OA(4943, 65, F49, 36) (dual of [65, 22, 37]-code) | [i] | ✔ | |
| 11 | Linear OA(4935, 65, F49, 28) (dual of [65, 30, 29]-code) | [i] | ✔ | |
| 12 | Linear OA(4947, 69, F49, 38) (dual of [69, 22, 39]-code) | [i] | ✔ | |
| 13 | Linear OA(4937, 69, F49, 28) (dual of [69, 32, 29]-code) | [i] | ✔ | |
| 14 | Linear OA(4951, 73, F49, 40) (dual of [73, 22, 41]-code) | [i] | ✔ | |
| 15 | Linear OA(4939, 73, F49, 28) (dual of [73, 34, 29]-code) | [i] | ✔ | |
| 16 | Linear OA(4955, 77, F49, 42) (dual of [77, 22, 43]-code) | [i] | ✔ | |
| 17 | Linear OA(4941, 77, F49, 28) (dual of [77, 36, 29]-code) | [i] | ✔ | |
| 18 | Linear OA(4933, 55, F49, 31) (dual of [55, 22, 32]-code) | [i] | ✔ | |
| 19 | Linear OA(4930, 55, F49, 28) (dual of [55, 25, 29]-code) | [i] | ✔ | |
| 20 | Linear OA(4945, 67, F49, 37) (dual of [67, 22, 38]-code) | [i] | ✔ | |
| 21 | Linear OA(4936, 67, F49, 28) (dual of [67, 31, 29]-code) | [i] | ✔ | |
| 22 | Linear OA(4937, 59, F49, 33) (dual of [59, 22, 34]-code) | [i] | ✔ | |
| 23 | Linear OA(4932, 59, F49, 28) (dual of [59, 27, 29]-code) | [i] | ✔ | |