Information on Result #657244
Linear OA(4925, 50, F49, 25) (dual of [50, 25, 26]-code or 50-arc in PG(24,49)), using algebraic-geometric code AG(F,12P) 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(750, 100, F7, 25) (dual of [100, 50, 26]-code) | [i] | Trace Code | |
| 2 | Linear OA(7100, 150, F7, 51) (dual of [150, 50, 52]-code) | [i] | Concatenation of Two Codes | |
| 3 | Linear OA(4928, 53, F49, 27) (dual of [53, 25, 28]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 4 | Linear OA(4926, 53, F49, 25) (dual of [53, 27, 26]-code) | [i] | ✔ | |
| 5 | Linear OA(4932, 57, F49, 29) (dual of [57, 25, 30]-code) | [i] | ✔ | |
| 6 | Linear OA(4928, 57, F49, 25) (dual of [57, 29, 26]-code) | [i] | ✔ | |
| 7 | Linear OA(4936, 61, F49, 31) (dual of [61, 25, 32]-code) | [i] | ✔ | |
| 8 | Linear OA(4930, 61, F49, 25) (dual of [61, 31, 26]-code) | [i] | ✔ | |
| 9 | Linear OA(4940, 65, F49, 33) (dual of [65, 25, 34]-code) | [i] | ✔ | |
| 10 | Linear OA(4932, 65, F49, 25) (dual of [65, 33, 26]-code) | [i] | ✔ | |
| 11 | Linear OA(4944, 69, F49, 35) (dual of [69, 25, 36]-code) | [i] | ✔ | |
| 12 | Linear OA(4934, 69, F49, 25) (dual of [69, 35, 26]-code) | [i] | ✔ | |
| 13 | Linear OA(4948, 73, F49, 37) (dual of [73, 25, 38]-code) | [i] | ✔ | |
| 14 | Linear OA(4936, 73, F49, 25) (dual of [73, 37, 26]-code) | [i] | ✔ | |
| 15 | Linear OA(4952, 77, F49, 39) (dual of [77, 25, 40]-code) | [i] | ✔ | |
| 16 | Linear OA(4930, 55, F49, 28) (dual of [55, 25, 29]-code) | [i] | ✔ | |
| 17 | Linear OA(4927, 55, F49, 25) (dual of [55, 28, 26]-code) | [i] | ✔ | |
| 18 | Linear OA(4942, 67, F49, 34) (dual of [67, 25, 35]-code) | [i] | ✔ | |
| 19 | Linear OA(4933, 67, F49, 25) (dual of [67, 34, 26]-code) | [i] | ✔ | |
| 20 | Linear OA(4954, 79, F49, 40) (dual of [79, 25, 41]-code) | [i] | ✔ | |
| 21 | Linear OA(4934, 59, F49, 30) (dual of [59, 25, 31]-code) | [i] | ✔ | |
| 22 | Linear OA(4929, 59, F49, 25) (dual of [59, 30, 26]-code) | [i] | ✔ | |