Information on Result #658027
Linear OA(2563, 257, F256, 3) (dual of [257, 254, 4]-code or 257-arc in PG(2,256) or 257-cap in PG(2,256)), using algebraic-geometric code AG(F, Q+125P) 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(25610, 514, F256, 7) (dual of [514, 504, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2569, 514, F256, 6) (dual of [514, 505, 7]-code) | [i] | ||
| 3 | Linear OA(25629, 65792, F256, 11) (dual of [65792, 65763, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 4 | Linear OA(25630, 65795, F256, 11) (dual of [65795, 65765, 12]-code) | [i] | ||
| 5 | Linear OA(25627, 65792, F256, 10) (dual of [65792, 65765, 11]-code) | [i] | ||
| 6 | Linear OA(25623, 65792, F256, 9) (dual of [65792, 65769, 10]-code) | [i] | ||
| 7 | Linear OA(25624, 65795, F256, 9) (dual of [65795, 65771, 10]-code) | [i] | ||
| 8 | Linear OA(25616, 65792, F256, 7) (dual of [65792, 65776, 8]-code) | [i] | ||
| 9 | Linear OA(25614, 65792, F256, 6) (dual of [65792, 65778, 7]-code) | [i] | ||
| 10 | Linear OA(2566, 260, F256, 5) (dual of [260, 254, 6]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 11 | Linear OA(25610, 264, F256, 7) (dual of [264, 254, 8]-code) | [i] | ✔ | |
| 12 | Linear OA(25614, 268, F256, 9) (dual of [268, 254, 10]-code) | [i] | ✔ | |
| 13 | Linear OA(2568, 262, F256, 6) (dual of [262, 254, 7]-code) | [i] | ✔ | |
| 14 | Linear OA(25612, 266, F256, 8) (dual of [266, 254, 9]-code) | [i] | ✔ | |
| 15 | Linear OA(25629, 66051, F256, 11) (dual of [66051, 66022, 12]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 16 | Linear OA(25627, 66050, F256, 10) (dual of [66050, 66023, 11]-code) | [i] | ||
| 17 | Linear OA(25624, 66051, F256, 9) (dual of [66051, 66027, 10]-code) | [i] | ||