Information on Result #657730
Linear OA(25642, 257, F256, 42) (dual of [257, 215, 43]-code or 257-arc in PG(41,256)), using algebraic-geometric code AG(F,107P) with degPÂ =Â 2 based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(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(1684, 514, F16, 42) (dual of [514, 430, 43]-code) | [i] | Trace Code | |
| 2 | OA(3268, 257, S32, 42) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6456, 257, S64, 42) | [i] | ||
| 4 | OA(12848, 257, S128, 42) | [i] | ||
| 5 | Linear OA(25663, 514, F256, 42) (dual of [514, 451, 43]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25645, 260, F256, 44) (dual of [260, 215, 45]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 7 | Linear OA(25643, 260, F256, 42) (dual of [260, 217, 43]-code) | [i] | ✔ | |
| 8 | Linear OA(25649, 264, F256, 46) (dual of [264, 215, 47]-code) | [i] | ✔ | |
| 9 | Linear OA(25645, 264, F256, 42) (dual of [264, 219, 43]-code) | [i] | ✔ | |
| 10 | Linear OA(25653, 268, F256, 48) (dual of [268, 215, 49]-code) | [i] | ✔ | |
| 11 | Linear OA(25647, 268, F256, 42) (dual of [268, 221, 43]-code) | [i] | ✔ | |
| 12 | Linear OA(25657, 272, F256, 50) (dual of [272, 215, 51]-code) | [i] | ✔ | |
| 13 | Linear OA(25649, 272, F256, 42) (dual of [272, 223, 43]-code) | [i] | ✔ | |
| 14 | Linear OA(25661, 276, F256, 52) (dual of [276, 215, 53]-code) | [i] | ✔ | |
| 15 | Linear OA(25651, 276, F256, 42) (dual of [276, 225, 43]-code) | [i] | ✔ | |
| 16 | Linear OA(25665, 280, F256, 54) (dual of [280, 215, 55]-code) | [i] | ✔ | |
| 17 | Linear OA(25653, 280, F256, 42) (dual of [280, 227, 43]-code) | [i] | ✔ | |
| 18 | Linear OA(25655, 284, F256, 42) (dual of [284, 229, 43]-code) | [i] | ✔ | |
| 19 | Linear OA(25657, 288, F256, 42) (dual of [288, 231, 43]-code) | [i] | ✔ | |
| 20 | Linear OA(25659, 292, F256, 42) (dual of [292, 233, 43]-code) | [i] | ✔ | |
| 21 | Linear OA(25661, 296, F256, 42) (dual of [296, 235, 43]-code) | [i] | ✔ | |
| 22 | Linear OA(25663, 300, F256, 42) (dual of [300, 237, 43]-code) | [i] | ✔ | |
| 23 | Linear OA(25665, 304, F256, 42) (dual of [304, 239, 43]-code) | [i] | ✔ | |
| 24 | Linear OA(25667, 308, F256, 42) (dual of [308, 241, 43]-code) | [i] | ✔ | |
| 25 | Linear OA(25647, 262, F256, 45) (dual of [262, 215, 46]-code) | [i] | ✔ | |
| 26 | Linear OA(25644, 262, F256, 42) (dual of [262, 218, 43]-code) | [i] | ✔ | |
| 27 | Linear OA(25659, 274, F256, 51) (dual of [274, 215, 52]-code) | [i] | ✔ | |
| 28 | Linear OA(25650, 274, F256, 42) (dual of [274, 224, 43]-code) | [i] | ✔ | |
| 29 | Linear OA(25656, 286, F256, 42) (dual of [286, 230, 43]-code) | [i] | ✔ | |
| 30 | Linear OA(25662, 298, F256, 42) (dual of [298, 236, 43]-code) | [i] | ✔ | |
| 31 | Linear OA(25668, 310, F256, 42) (dual of [310, 242, 43]-code) | [i] | ✔ | |
| 32 | Linear OA(25651, 266, F256, 47) (dual of [266, 215, 48]-code) | [i] | ✔ | |
| 33 | Linear OA(25646, 266, F256, 42) (dual of [266, 220, 43]-code) | [i] | ✔ | |
| 34 | Linear OA(25666, 306, F256, 42) (dual of [306, 240, 43]-code) | [i] | ✔ | |