Information on Result #657608
Linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using algebraic-geometric code AG(F, Q+13P) with degQ = 4 and degPÂ =Â 3 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(712, 100, F7, 6) (dual of [100, 88, 7]-code) | [i] | Trace Code | |
| 2 | Linear OA(711, 50, F7, 6) (dual of [50, 39, 7]-code) | [i] | Base Reduction for Projective Spaces | |
| 3 | Linear OA(4920, 103, F49, 13) (dual of [103, 83, 14]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(4931, 2452, F49, 13) (dual of [2452, 2421, 14]-code) | [i] | ||
| 5 | Linear OA(4943, 117700, F49, 13) (dual of [117700, 117657, 14]-code) | [i] | ||
| 6 | Linear OA(4955, 5764852, F49, 13) (dual of [5764852, 5764797, 14]-code) | [i] | ||
| 7 | Linear OA(4918, 100, F49, 12) (dual of [100, 82, 13]-code) | [i] | ||
| 8 | Linear OA(4919, 103, F49, 12) (dual of [103, 84, 13]-code) | [i] | ||
| 9 | Linear OA(4929, 2451, F49, 12) (dual of [2451, 2422, 13]-code) | [i] | ||
| 10 | Linear OA(4940, 117699, F49, 12) (dual of [117699, 117659, 13]-code) | [i] | ||
| 11 | Linear OA(4951, 5764851, F49, 12) (dual of [5764851, 5764800, 13]-code) | [i] | ||
| 12 | Linear OA(4931, 2453, F49, 13) (dual of [2453, 2422, 14]-code) | [i] | ||
| 13 | Linear OA(4932, 2457, F49, 13) (dual of [2457, 2425, 14]-code) | [i] | ||
| 14 | Linear OA(4943, 117702, F49, 13) (dual of [117702, 117659, 14]-code) | [i] | ||
| 15 | Linear OA(4944, 117707, F49, 13) (dual of [117707, 117663, 14]-code) | [i] | ||
| 16 | Linear OA(4955, 5764855, F49, 13) (dual of [5764855, 5764800, 14]-code) | [i] | ||
| 17 | Linear OA(4929, 2453, F49, 12) (dual of [2453, 2424, 13]-code) | [i] | ||
| 18 | Linear OA(4940, 117702, F49, 12) (dual of [117702, 117662, 13]-code) | [i] | ||
| 19 | Linear OA(4941, 117706, F49, 12) (dual of [117706, 117665, 13]-code) | [i] | ||
| 20 | Linear OA(4942, 117710, F49, 12) (dual of [117710, 117668, 13]-code) | [i] | ||
| 21 | Linear OA(4951, 5764855, F49, 12) (dual of [5764855, 5764804, 13]-code) | [i] | ||
| 22 | Linear OA(4952, 5764860, F49, 12) (dual of [5764860, 5764808, 13]-code) | [i] | ||
| 23 | Linear OA(4953, 5764865, F49, 12) (dual of [5764865, 5764812, 13]-code) | [i] | ||
| 24 | Linear OA(4920, 114, F49, 13) (dual of [114, 94, 14]-code) | [i] | ||
| 25 | Linear OA(4919, 114, F49, 12) (dual of [114, 95, 13]-code) | [i] | ||
| 26 | Linear OA(4914, 2450, F49, 6) (dual of [2450, 2436, 7]-code) | [i] | Generalized (u, u+v)-Construction | |
| 27 | Linear OA(4955, 2501, F49, 20) (dual of [2501, 2446, 21]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 28 | Linear OA(4952, 2502, F49, 19) (dual of [2502, 2450, 20]-code) | [i] | ||
| 29 | Linear OA(4953, 2505, F49, 19) (dual of [2505, 2452, 20]-code) | [i] | ||
| 30 | Linear OA(4950, 2501, F49, 18) (dual of [2501, 2451, 19]-code) | [i] | ||
| 31 | Linear OA(4935, 2502, F49, 13) (dual of [2502, 2467, 14]-code) | [i] | ||
| 32 | Linear OA(4947, 117750, F49, 13) (dual of [117750, 117703, 14]-code) | [i] | ||
| 33 | Linear OA(4944, 117749, F49, 12) (dual of [117749, 117705, 13]-code) | [i] | ||
| 34 | Linear OA(4955, 5764901, F49, 12) (dual of [5764901, 5764846, 13]-code) | [i] | ||