Information on Result #618455
Linear OA(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound)
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]
- 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(710, 100, F7, 5) (dual of [100, 90, 6]-code) | [i] | Trace Code | |
| 2 | Linear OA(4916, 100, F49, 11) (dual of [100, 84, 12]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4917, 103, F49, 11) (dual of [103, 86, 12]-code) | [i] | ||
| 4 | Linear OA(4926, 2452, F49, 11) (dual of [2452, 2426, 12]-code) | [i] | ||
| 5 | Linear OA(4936, 117700, F49, 11) (dual of [117700, 117664, 12]-code) | [i] | ||
| 6 | Linear OA(4946, 5764852, F49, 11) (dual of [5764852, 5764806, 12]-code) | [i] | ||
| 7 | Linear OA(4916, 103, F49, 10) (dual of [103, 87, 11]-code) | [i] | ||
| 8 | Linear OA(4924, 2451, F49, 10) (dual of [2451, 2427, 11]-code) | [i] | ||
| 9 | Linear OA(4933, 117699, F49, 10) (dual of [117699, 117666, 11]-code) | [i] | ||
| 10 | Linear OA(4942, 5764851, F49, 10) (dual of [5764851, 5764809, 11]-code) | [i] | ||
| 11 | Linear OA(4926, 2453, F49, 11) (dual of [2453, 2427, 12]-code) | [i] | ||
| 12 | Linear OA(4927, 2457, F49, 11) (dual of [2457, 2430, 12]-code) | [i] | ||
| 13 | Linear OA(4936, 117702, F49, 11) (dual of [117702, 117666, 12]-code) | [i] | ||
| 14 | Linear OA(4937, 117707, F49, 11) (dual of [117707, 117670, 12]-code) | [i] | ||
| 15 | Linear OA(4946, 5764855, F49, 11) (dual of [5764855, 5764809, 12]-code) | [i] | ||
| 16 | Linear OA(4947, 5764861, F49, 11) (dual of [5764861, 5764814, 12]-code) | [i] | ||
| 17 | Linear OA(4924, 2453, F49, 10) (dual of [2453, 2429, 11]-code) | [i] | ||
| 18 | Linear OA(4933, 117702, F49, 10) (dual of [117702, 117669, 11]-code) | [i] | ||
| 19 | Linear OA(4934, 117706, F49, 10) (dual of [117706, 117672, 11]-code) | [i] | ||
| 20 | Linear OA(4942, 5764855, F49, 10) (dual of [5764855, 5764813, 11]-code) | [i] | ||
| 21 | Linear OA(4943, 5764860, F49, 10) (dual of [5764860, 5764817, 11]-code) | [i] | ||
| 22 | Linear OA(4917, 114, F49, 11) (dual of [114, 97, 12]-code) | [i] | ||
| 23 | Linear OA(4916, 114, F49, 10) (dual of [114, 98, 11]-code) | [i] | ||
| 24 | Linear OA(4929, 2450, F49, 11) (dual of [2450, 2421, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 25 | Linear OA(4910, 2450, F49, 5) (dual of [2450, 2440, 6]-code) | [i] | ||
| 26 | Linear OA(4946, 2502, F49, 17) (dual of [2502, 2456, 18]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 27 | Linear OA(4947, 2505, F49, 17) (dual of [2505, 2458, 18]-code) | [i] | ||
| 28 | Linear OA(4944, 2501, F49, 16) (dual of [2501, 2457, 17]-code) | [i] | ||
| 29 | Linear OA(4941, 2502, F49, 15) (dual of [2502, 2461, 16]-code) | [i] | ||
| 30 | Linear OA(4955, 117750, F49, 15) (dual of [117750, 117695, 16]-code) | [i] | ||
| 31 | Linear OA(4929, 2502, F49, 11) (dual of [2502, 2473, 12]-code) | [i] | ||
| 32 | Linear OA(4939, 117750, F49, 11) (dual of [117750, 117711, 12]-code) | [i] | ||
| 33 | Linear OA(4949, 5764902, F49, 11) (dual of [5764902, 5764853, 12]-code) | [i] | ||
| 34 | Linear OA(4936, 117749, F49, 10) (dual of [117749, 117713, 11]-code) | [i] | ||
| 35 | Linear OA(4945, 5764901, F49, 10) (dual of [5764901, 5764856, 11]-code) | [i] | ||
| 36 | Linear OA(496, 52, F49, 5) (dual of [52, 46, 6]-code) | [i] | ✔ | Construction X with Cyclic Codes |