Information on Result #657258
Linear OA(4911, 50, F49, 11) (dual of [50, 39, 12]-code or 50-arc in PG(10,49)), using algebraic-geometric code AG(F,19P) 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(722, 100, F7, 11) (dual of [100, 78, 12]-code) | [i] | Trace Code | |
| 2 | Linear OA(4934, 100, F49, 23) (dual of [100, 66, 24]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4935, 103, F49, 23) (dual of [103, 68, 24]-code) | [i] | ||
| 4 | Linear OA(4934, 103, F49, 22) (dual of [103, 69, 23]-code) | [i] | ||
| 5 | Linear OA(4954, 2451, F49, 22) (dual of [2451, 2397, 23]-code) | [i] | ||
| 6 | Linear OA(4916, 100, F49, 11) (dual of [100, 84, 12]-code) | [i] | ||
| 7 | Linear OA(4954, 2453, F49, 22) (dual of [2453, 2399, 23]-code) | [i] | ||
| 8 | Linear OA(4935, 114, F49, 23) (dual of [114, 79, 24]-code) | [i] | ||
| 9 | Linear OA(4934, 114, F49, 22) (dual of [114, 80, 23]-code) | [i] | ||
| 10 | Linear OA(4929, 2450, F49, 11) (dual of [2450, 2421, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 11 | Linear OA(4914, 53, F49, 13) (dual of [53, 39, 14]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 12 | Linear OA(4912, 53, F49, 11) (dual of [53, 41, 12]-code) | [i] | ✔ | |
| 13 | Linear OA(4918, 57, F49, 15) (dual of [57, 39, 16]-code) | [i] | ✔ | |
| 14 | Linear OA(4914, 57, F49, 11) (dual of [57, 43, 12]-code) | [i] | ✔ | |
| 15 | Linear OA(4922, 61, F49, 17) (dual of [61, 39, 18]-code) | [i] | ✔ | |
| 16 | Linear OA(4926, 65, F49, 19) (dual of [65, 39, 20]-code) | [i] | ✔ | |
| 17 | Linear OA(4930, 69, F49, 21) (dual of [69, 39, 22]-code) | [i] | ✔ | |
| 18 | Linear OA(4916, 55, F49, 14) (dual of [55, 39, 15]-code) | [i] | ✔ | |
| 19 | Linear OA(4913, 55, F49, 11) (dual of [55, 42, 12]-code) | [i] | ✔ | |
| 20 | Linear OA(4928, 67, F49, 20) (dual of [67, 39, 21]-code) | [i] | ✔ | |
| 21 | Linear OA(4920, 59, F49, 16) (dual of [59, 39, 17]-code) | [i] | ✔ | |
| 22 | Linear OA(4915, 59, F49, 11) (dual of [59, 44, 12]-code) | [i] | ✔ | |