Information on Result #657979
Linear OA(25651, 257, F256, 51) (dual of [257, 206, 52]-code or 257-arc in PG(50,256)), using algebraic-geometric code AG(F, Q+101P) with degQ = 3 and 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(16102, 514, F16, 51) (dual of [514, 412, 52]-code) | [i] | Trace Code | |
| 2 | OA(3282, 257, S32, 51) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6468, 257, S64, 51) | [i] | ||
| 4 | OA(12859, 257, S128, 51) | [i] | ||
| 5 | Linear OA(25654, 260, F256, 53) (dual of [260, 206, 54]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 6 | Linear OA(25652, 260, F256, 51) (dual of [260, 208, 52]-code) | [i] | ✔ | |
| 7 | Linear OA(25658, 264, F256, 55) (dual of [264, 206, 56]-code) | [i] | ✔ | |
| 8 | Linear OA(25654, 264, F256, 51) (dual of [264, 210, 52]-code) | [i] | ✔ | |
| 9 | Linear OA(25662, 268, F256, 57) (dual of [268, 206, 58]-code) | [i] | ✔ | |
| 10 | Linear OA(25656, 268, F256, 51) (dual of [268, 212, 52]-code) | [i] | ✔ | |
| 11 | Linear OA(25666, 272, F256, 59) (dual of [272, 206, 60]-code) | [i] | ✔ | |
| 12 | Linear OA(25658, 272, F256, 51) (dual of [272, 214, 52]-code) | [i] | ✔ | |
| 13 | Linear OA(25660, 276, F256, 51) (dual of [276, 216, 52]-code) | [i] | ✔ | |
| 14 | Linear OA(25662, 280, F256, 51) (dual of [280, 218, 52]-code) | [i] | ✔ | |
| 15 | Linear OA(25664, 284, F256, 51) (dual of [284, 220, 52]-code) | [i] | ✔ | |
| 16 | Linear OA(25666, 288, F256, 51) (dual of [288, 222, 52]-code) | [i] | ✔ | |
| 17 | Linear OA(25668, 292, F256, 51) (dual of [292, 224, 52]-code) | [i] | ✔ | |
| 18 | Linear OA(25656, 262, F256, 54) (dual of [262, 206, 55]-code) | [i] | ✔ | |
| 19 | Linear OA(25653, 262, F256, 51) (dual of [262, 209, 52]-code) | [i] | ✔ | |
| 20 | Linear OA(25668, 274, F256, 60) (dual of [274, 206, 61]-code) | [i] | ✔ | |
| 21 | Linear OA(25659, 274, F256, 51) (dual of [274, 215, 52]-code) | [i] | ✔ | |
| 22 | Linear OA(25665, 286, F256, 51) (dual of [286, 221, 52]-code) | [i] | ✔ | |
| 23 | Linear OA(25660, 266, F256, 56) (dual of [266, 206, 57]-code) | [i] | ✔ | |
| 24 | Linear OA(25655, 266, F256, 51) (dual of [266, 211, 52]-code) | [i] | ✔ | |