Information on Result #657391
Linear OA(4912, 50, F49, 12) (dual of [50, 38, 13]-code or 50-arc in PG(11,49)), using algebraic-geometric code AG(F, Q+17P) 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(724, 100, F7, 12) (dual of [100, 76, 13]-code) | [i] | Trace Code | |
| 2 | Linear OA(4938, 103, F49, 25) (dual of [103, 65, 26]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4936, 100, F49, 24) (dual of [100, 64, 25]-code) | [i] | ||
| 4 | Linear OA(4937, 103, F49, 24) (dual of [103, 66, 25]-code) | [i] | ||
| 5 | Linear OA(4918, 100, F49, 12) (dual of [100, 82, 13]-code) | [i] | ||
| 6 | Linear OA(4938, 114, F49, 25) (dual of [114, 76, 26]-code) | [i] | ||
| 7 | Linear OA(4915, 53, F49, 14) (dual of [53, 38, 15]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 8 | Linear OA(4913, 53, F49, 12) (dual of [53, 40, 13]-code) | [i] | ✔ | |
| 9 | Linear OA(4919, 57, F49, 16) (dual of [57, 38, 17]-code) | [i] | ✔ | |
| 10 | Linear OA(4915, 57, F49, 12) (dual of [57, 42, 13]-code) | [i] | ✔ | |
| 11 | Linear OA(4923, 61, F49, 18) (dual of [61, 38, 19]-code) | [i] | ✔ | |
| 12 | Linear OA(4917, 61, F49, 12) (dual of [61, 44, 13]-code) | [i] | ✔ | |
| 13 | Linear OA(4927, 65, F49, 20) (dual of [65, 38, 21]-code) | [i] | ✔ | |
| 14 | Linear OA(4931, 69, F49, 22) (dual of [69, 38, 23]-code) | [i] | ✔ | |
| 15 | Linear OA(4935, 73, F49, 24) (dual of [73, 38, 25]-code) | [i] | ✔ | |
| 16 | Linear OA(4917, 55, F49, 15) (dual of [55, 38, 16]-code) | [i] | ✔ | |
| 17 | Linear OA(4914, 55, F49, 12) (dual of [55, 41, 13]-code) | [i] | ✔ | |
| 18 | Linear OA(4929, 67, F49, 21) (dual of [67, 38, 22]-code) | [i] | ✔ | |
| 19 | Linear OA(4921, 59, F49, 17) (dual of [59, 38, 18]-code) | [i] | ✔ | |
| 20 | Linear OA(4916, 59, F49, 12) (dual of [59, 43, 13]-code) | [i] | ✔ | |