Information on Result #657387
Linear OA(4916, 50, F49, 16) (dual of [50, 34, 17]-code or 50-arc in PG(15,49)), using algebraic-geometric code AG(F, Q+15P) 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(732, 100, F7, 16) (dual of [100, 68, 17]-code) | [i] | Trace Code | |
| 2 | Linear OA(4950, 103, F49, 33) (dual of [103, 53, 34]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4948, 100, F49, 32) (dual of [100, 52, 33]-code) | [i] | ||
| 4 | Linear OA(4949, 103, F49, 32) (dual of [103, 54, 33]-code) | [i] | ||
| 5 | Linear OA(4924, 100, F49, 16) (dual of [100, 76, 17]-code) | [i] | ||
| 6 | Linear OA(4919, 53, F49, 18) (dual of [53, 34, 19]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 7 | Linear OA(4917, 53, F49, 16) (dual of [53, 36, 17]-code) | [i] | ✔ | |
| 8 | Linear OA(4923, 57, F49, 20) (dual of [57, 34, 21]-code) | [i] | ✔ | |
| 9 | Linear OA(4919, 57, F49, 16) (dual of [57, 38, 17]-code) | [i] | ✔ | |
| 10 | Linear OA(4927, 61, F49, 22) (dual of [61, 34, 23]-code) | [i] | ✔ | |
| 11 | Linear OA(4921, 61, F49, 16) (dual of [61, 40, 17]-code) | [i] | ✔ | |
| 12 | Linear OA(4931, 65, F49, 24) (dual of [65, 34, 25]-code) | [i] | ✔ | |
| 13 | Linear OA(4923, 65, F49, 16) (dual of [65, 42, 17]-code) | [i] | ✔ | |
| 14 | Linear OA(4935, 69, F49, 26) (dual of [69, 34, 27]-code) | [i] | ✔ | |
| 15 | Linear OA(4939, 73, F49, 28) (dual of [73, 34, 29]-code) | [i] | ✔ | |
| 16 | Linear OA(4943, 77, F49, 30) (dual of [77, 34, 31]-code) | [i] | ✔ | |
| 17 | Linear OA(4947, 81, F49, 32) (dual of [81, 34, 33]-code) | [i] | ✔ | |
| 18 | Linear OA(4921, 55, F49, 19) (dual of [55, 34, 20]-code) | [i] | ✔ | |
| 19 | Linear OA(4918, 55, F49, 16) (dual of [55, 37, 17]-code) | [i] | ✔ | |
| 20 | Linear OA(4933, 67, F49, 25) (dual of [67, 34, 26]-code) | [i] | ✔ | |
| 21 | Linear OA(4945, 79, F49, 31) (dual of [79, 34, 32]-code) | [i] | ✔ | |
| 22 | Linear OA(4925, 59, F49, 21) (dual of [59, 34, 22]-code) | [i] | ✔ | |
| 23 | Linear OA(4920, 59, F49, 16) (dual of [59, 39, 17]-code) | [i] | ✔ | |