Information on Result #657768
Linear OA(2564, 257, F256, 4) (dual of [257, 253, 5]-code or 257-arc in PG(3,256)), using algebraic-geometric code AG(F,126P) 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(168, 514, F16, 4) (dual of [514, 506, 5]-code) | [i] | Trace Code | |
| 2 | Linear OA(167, 257, F16, 4) (dual of [257, 250, 5]-code) | [i] | Base Reduction for Projective Spaces | |
| 3 | OA(1285, 257, S128, 4) | [i] | Discarding Parts of the Base for OAs | |
| 4 | Linear OA(25613, 514, F256, 9) (dual of [514, 501, 10]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(25614, 517, F256, 9) (dual of [517, 503, 10]-code) | [i] | ||
| 6 | Linear OA(25621, 65794, F256, 9) (dual of [65794, 65773, 10]-code) | [i] | ||
| 7 | Linear OA(25612, 514, F256, 8) (dual of [514, 502, 9]-code) | [i] | ||
| 8 | Linear OA(25619, 65793, F256, 8) (dual of [65793, 65774, 9]-code) | [i] | ||
| 9 | Linear OA(25621, 65795, F256, 9) (dual of [65795, 65774, 10]-code) | [i] | ||
| 10 | Linear OA(25622, 65799, F256, 9) (dual of [65799, 65777, 10]-code) | [i] | ||
| 11 | Linear OA(25619, 65795, F256, 8) (dual of [65795, 65776, 9]-code) | [i] | ||
| 12 | Linear OA(25614, 546, F256, 9) (dual of [546, 532, 10]-code) | [i] | ||
| 13 | Linear OA(25623, 65792, F256, 9) (dual of [65792, 65769, 10]-code) | [i] | Generalized (u, u+v)-Construction | |
| 14 | Linear OA(25624, 65795, F256, 9) (dual of [65795, 65771, 10]-code) | [i] | ||
| 15 | Linear OA(25620, 65792, F256, 8) (dual of [65792, 65772, 9]-code) | [i] | ||
| 16 | Linear OA(25621, 65795, F256, 8) (dual of [65795, 65774, 9]-code) | [i] | ||
| 17 | Linear OA(2568, 65792, F256, 4) (dual of [65792, 65784, 5]-code) | [i] | ||
| 18 | Linear OA(2567, 260, F256, 6) (dual of [260, 253, 7]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 19 | Linear OA(2565, 260, F256, 4) (dual of [260, 255, 5]-code) | [i] | ✔ | |
| 20 | Linear OA(25611, 264, F256, 8) (dual of [264, 253, 9]-code) | [i] | ✔ | |
| 21 | Linear OA(25615, 268, F256, 10) (dual of [268, 253, 11]-code) | [i] | ✔ | |
| 22 | Linear OA(25619, 272, F256, 12) (dual of [272, 253, 13]-code) | [i] | ✔ | |
| 23 | Linear OA(2569, 262, F256, 7) (dual of [262, 253, 8]-code) | [i] | ✔ | |
| 24 | Linear OA(25613, 266, F256, 9) (dual of [266, 253, 10]-code) | [i] | ✔ | |
| 25 | Linear OA(25638, 66050, F256, 14) (dual of [66050, 66012, 15]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 26 | Linear OA(25639, 66053, F256, 14) (dual of [66053, 66014, 15]-code) | [i] | ||
| 27 | Linear OA(25635, 66051, F256, 13) (dual of [66051, 66016, 14]-code) | [i] | ||
| 28 | Linear OA(25636, 66054, F256, 13) (dual of [66054, 66018, 14]-code) | [i] | ||
| 29 | Linear OA(25633, 66050, F256, 12) (dual of [66050, 66017, 13]-code) | [i] | ||
| 30 | Linear OA(25624, 66051, F256, 9) (dual of [66051, 66027, 10]-code) | [i] | ||
| 31 | Linear OA(25621, 66050, F256, 8) (dual of [66050, 66029, 9]-code) | [i] | ||