Information on Result #657238
Linear OA(4931, 50, F49, 31) (dual of [50, 19, 32]-code or 50-arc in PG(30,49)), using algebraic-geometric code AG(F,9P) with 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]
- Expurgated Narrow-Sense BCH-Codes (BCH-Bound) [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(762, 100, F7, 31) (dual of [100, 38, 32]-code) | [i] | Trace Code | |
| 2 | Linear OA(4946, 100, F49, 31) (dual of [100, 54, 32]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4934, 53, F49, 33) (dual of [53, 19, 34]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 4 | Linear OA(4932, 53, F49, 31) (dual of [53, 21, 32]-code) | [i] | ✔ | |
| 5 | Linear OA(4938, 57, F49, 35) (dual of [57, 19, 36]-code) | [i] | ✔ | |
| 6 | Linear OA(4934, 57, F49, 31) (dual of [57, 23, 32]-code) | [i] | ✔ | |
| 7 | Linear OA(4942, 61, F49, 37) (dual of [61, 19, 38]-code) | [i] | ✔ | |
| 8 | Linear OA(4936, 61, F49, 31) (dual of [61, 25, 32]-code) | [i] | ✔ | |
| 9 | Linear OA(4946, 65, F49, 39) (dual of [65, 19, 40]-code) | [i] | ✔ | |
| 10 | Linear OA(4938, 65, F49, 31) (dual of [65, 27, 32]-code) | [i] | ✔ | |
| 11 | Linear OA(4950, 69, F49, 41) (dual of [69, 19, 42]-code) | [i] | ✔ | |
| 12 | Linear OA(4940, 69, F49, 31) (dual of [69, 29, 32]-code) | [i] | ✔ | |
| 13 | Linear OA(4954, 73, F49, 43) (dual of [73, 19, 44]-code) | [i] | ✔ | |
| 14 | Linear OA(4942, 73, F49, 31) (dual of [73, 31, 32]-code) | [i] | ✔ | |
| 15 | Linear OA(4944, 77, F49, 31) (dual of [77, 33, 32]-code) | [i] | ✔ | |
| 16 | Linear OA(4936, 55, F49, 34) (dual of [55, 19, 35]-code) | [i] | ✔ | |
| 17 | Linear OA(4933, 55, F49, 31) (dual of [55, 22, 32]-code) | [i] | ✔ | |
| 18 | Linear OA(4948, 67, F49, 40) (dual of [67, 19, 41]-code) | [i] | ✔ | |
| 19 | Linear OA(4939, 67, F49, 31) (dual of [67, 28, 32]-code) | [i] | ✔ | |
| 20 | Linear OA(4945, 79, F49, 31) (dual of [79, 34, 32]-code) | [i] | ✔ | |
| 21 | Linear OA(4940, 59, F49, 36) (dual of [59, 19, 37]-code) | [i] | ✔ | |
| 22 | Linear OA(4935, 59, F49, 31) (dual of [59, 24, 32]-code) | [i] | ✔ | |