Information on Result #657764
Linear OA(2568, 257, F256, 8) (dual of [257, 249, 9]-code or 257-arc in PG(7,256)), using algebraic-geometric code AG(F,124P) 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(432, 1028, F4, 8) (dual of [1028, 996, 9]-code) | [i] | Trace Code | |
| 2 | Linear OA(1616, 514, F16, 8) (dual of [514, 498, 9]-code) | [i] | ||
| 3 | Linear OA(1615, 257, F16, 8) (dual of [257, 242, 9]-code) | [i] | Base Reduction for Projective Spaces | |
| 4 | OA(3213, 257, S32, 8) | [i] | Discarding Parts of the Base for OAs | |
| 5 | OA(6411, 257, S64, 8) | [i] | ||
| 6 | OA(12810, 257, S128, 8) | [i] | ||
| 7 | Linear OA(25625, 514, F256, 17) (dual of [514, 489, 18]-code) | [i] | (u, u+v)-Construction | |
| 8 | Linear OA(25626, 517, F256, 17) (dual of [517, 491, 18]-code) | [i] | ||
| 9 | Linear OA(25641, 65794, F256, 17) (dual of [65794, 65753, 18]-code) | [i] | ||
| 10 | Linear OA(25624, 514, F256, 16) (dual of [514, 490, 17]-code) | [i] | ||
| 11 | Linear OA(25625, 517, F256, 16) (dual of [517, 492, 17]-code) | [i] | ||
| 12 | Linear OA(25639, 65793, F256, 16) (dual of [65793, 65754, 17]-code) | [i] | ||
| 13 | Linear OA(25612, 514, F256, 8) (dual of [514, 502, 9]-code) | [i] | ||
| 14 | Linear OA(25641, 65795, F256, 17) (dual of [65795, 65754, 18]-code) | [i] | ||
| 15 | Linear OA(25642, 65799, F256, 17) (dual of [65799, 65757, 18]-code) | [i] | ||
| 16 | Linear OA(25644, 65805, F256, 17) (dual of [65805, 65761, 18]-code) | [i] | ||
| 17 | Linear OA(25639, 65795, F256, 16) (dual of [65795, 65756, 17]-code) | [i] | ||
| 18 | Linear OA(25626, 546, F256, 17) (dual of [546, 520, 18]-code) | [i] | ||
| 19 | Linear OA(25625, 546, F256, 16) (dual of [546, 521, 17]-code) | [i] | ||
| 20 | Linear OA(25620, 65792, F256, 8) (dual of [65792, 65772, 9]-code) | [i] | Generalized (u, u+v)-Construction | |
| 21 | Linear OA(25611, 260, F256, 10) (dual of [260, 249, 11]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 22 | Linear OA(2569, 260, F256, 8) (dual of [260, 251, 9]-code) | [i] | ✔ | |
| 23 | Linear OA(25615, 264, F256, 12) (dual of [264, 249, 13]-code) | [i] | ✔ | |
| 24 | Linear OA(25611, 264, F256, 8) (dual of [264, 253, 9]-code) | [i] | ✔ | |
| 25 | Linear OA(25619, 268, F256, 14) (dual of [268, 249, 15]-code) | [i] | ✔ | |
| 26 | Linear OA(25623, 272, F256, 16) (dual of [272, 249, 17]-code) | [i] | ✔ | |
| 27 | Linear OA(25627, 276, F256, 18) (dual of [276, 249, 19]-code) | [i] | ✔ | |
| 28 | Linear OA(25631, 280, F256, 20) (dual of [280, 249, 21]-code) | [i] | ✔ | |
| 29 | Linear OA(25635, 284, F256, 22) (dual of [284, 249, 23]-code) | [i] | ✔ | |
| 30 | Linear OA(25639, 288, F256, 24) (dual of [288, 249, 25]-code) | [i] | ✔ | |
| 31 | Linear OA(25613, 262, F256, 11) (dual of [262, 249, 12]-code) | [i] | ✔ | |
| 32 | Linear OA(25610, 262, F256, 8) (dual of [262, 252, 9]-code) | [i] | ✔ | |
| 33 | Linear OA(25625, 274, F256, 17) (dual of [274, 249, 18]-code) | [i] | ✔ | |
| 34 | Linear OA(25637, 286, F256, 23) (dual of [286, 249, 24]-code) | [i] | ✔ | |
| 35 | Linear OA(25617, 266, F256, 13) (dual of [266, 249, 14]-code) | [i] | ✔ | |
| 36 | Linear OA(25612, 266, F256, 8) (dual of [266, 254, 9]-code) | [i] | ✔ | |
| 37 | Linear OA(25667, 66050, F256, 24) (dual of [66050, 65983, 25]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 38 | Linear OA(25668, 66053, F256, 24) (dual of [66053, 65985, 25]-code) | [i] | ||
| 39 | Linear OA(25646, 66051, F256, 17) (dual of [66051, 66005, 18]-code) | [i] | ||
| 40 | Linear OA(25644, 66050, F256, 16) (dual of [66050, 66006, 17]-code) | [i] | ||