Information on Result #657254
Linear OA(4915, 50, F49, 15) (dual of [50, 35, 16]-code or 50-arc in PG(14,49)), using algebraic-geometric code AG(F,17P) 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(730, 100, F7, 15) (dual of [100, 70, 16]-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(4947, 103, F49, 31) (dual of [103, 56, 32]-code) | [i] | ||
| 4 | Linear OA(4946, 103, F49, 30) (dual of [103, 57, 31]-code) | [i] | ||
| 5 | Linear OA(4922, 100, F49, 15) (dual of [100, 78, 16]-code) | [i] | ||
| 6 | Linear OA(4918, 53, F49, 17) (dual of [53, 35, 18]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 7 | Linear OA(4916, 53, F49, 15) (dual of [53, 37, 16]-code) | [i] | ✔ | |
| 8 | Linear OA(4922, 57, F49, 19) (dual of [57, 35, 20]-code) | [i] | ✔ | |
| 9 | Linear OA(4918, 57, F49, 15) (dual of [57, 39, 16]-code) | [i] | ✔ | |
| 10 | Linear OA(4926, 61, F49, 21) (dual of [61, 35, 22]-code) | [i] | ✔ | |
| 11 | Linear OA(4920, 61, F49, 15) (dual of [61, 41, 16]-code) | [i] | ✔ | |
| 12 | Linear OA(4930, 65, F49, 23) (dual of [65, 35, 24]-code) | [i] | ✔ | |
| 13 | Linear OA(4934, 69, F49, 25) (dual of [69, 35, 26]-code) | [i] | ✔ | |
| 14 | Linear OA(4938, 73, F49, 27) (dual of [73, 35, 28]-code) | [i] | ✔ | |
| 15 | Linear OA(4942, 77, F49, 29) (dual of [77, 35, 30]-code) | [i] | ✔ | |
| 16 | Linear OA(4920, 55, F49, 18) (dual of [55, 35, 19]-code) | [i] | ✔ | |
| 17 | Linear OA(4917, 55, F49, 15) (dual of [55, 38, 16]-code) | [i] | ✔ | |
| 18 | Linear OA(4932, 67, F49, 24) (dual of [67, 35, 25]-code) | [i] | ✔ | |
| 19 | Linear OA(4944, 79, F49, 30) (dual of [79, 35, 31]-code) | [i] | ✔ | |
| 20 | Linear OA(4924, 59, F49, 20) (dual of [59, 35, 21]-code) | [i] | ✔ | |
| 21 | Linear OA(4919, 59, F49, 15) (dual of [59, 40, 16]-code) | [i] | ✔ | |