Information on Result #658025
Linear OA(2565, 257, F256, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using algebraic-geometric code AG(F, Q+124P) 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]
- Expurgated Narrow-Sense BCH-Codes (BCH-Bound) [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(1610, 514, F16, 5) (dual of [514, 504, 6]-code) | [i] | Trace Code | |
| 2 | OA(1286, 257, S128, 5) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(25616, 514, F256, 11) (dual of [514, 498, 12]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(25617, 517, F256, 11) (dual of [517, 500, 12]-code) | [i] | ||
| 5 | Linear OA(25626, 65794, F256, 11) (dual of [65794, 65768, 12]-code) | [i] | ||
| 6 | Linear OA(25615, 514, F256, 10) (dual of [514, 499, 11]-code) | [i] | ||
| 7 | Linear OA(25624, 65793, F256, 10) (dual of [65793, 65769, 11]-code) | [i] | ||
| 8 | Linear OA(25626, 65795, F256, 11) (dual of [65795, 65769, 12]-code) | [i] | ||
| 9 | Linear OA(25627, 65799, F256, 11) (dual of [65799, 65772, 12]-code) | [i] | ||
| 10 | Linear OA(25624, 65795, F256, 10) (dual of [65795, 65771, 11]-code) | [i] | ||
| 11 | Linear OA(25617, 546, F256, 11) (dual of [546, 529, 12]-code) | [i] | ||
| 12 | Linear OA(25629, 65792, F256, 11) (dual of [65792, 65763, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 13 | Linear OA(25630, 65795, F256, 11) (dual of [65795, 65765, 12]-code) | [i] | ||
| 14 | Linear OA(25627, 65792, F256, 10) (dual of [65792, 65765, 11]-code) | [i] | ||
| 15 | Linear OA(25610, 65792, F256, 5) (dual of [65792, 65782, 6]-code) | [i] | ||
| 16 | Linear OA(2568, 260, F256, 7) (dual of [260, 252, 8]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 17 | Linear OA(2566, 260, F256, 5) (dual of [260, 254, 6]-code) | [i] | ✔ | |
| 18 | Linear OA(25612, 264, F256, 9) (dual of [264, 252, 10]-code) | [i] | ✔ | |
| 19 | Linear OA(25616, 268, F256, 11) (dual of [268, 252, 12]-code) | [i] | ✔ | |
| 20 | Linear OA(25620, 272, F256, 13) (dual of [272, 252, 14]-code) | [i] | ✔ | |
| 21 | Linear OA(25624, 276, F256, 15) (dual of [276, 252, 16]-code) | [i] | ✔ | |
| 22 | Linear OA(25610, 262, F256, 8) (dual of [262, 252, 9]-code) | [i] | ✔ | |
| 23 | Linear OA(25622, 274, F256, 14) (dual of [274, 252, 15]-code) | [i] | ✔ | |
| 24 | Linear OA(25614, 266, F256, 10) (dual of [266, 252, 11]-code) | [i] | ✔ | |
| 25 | Linear OA(25646, 66051, F256, 17) (dual of [66051, 66005, 18]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 26 | Linear OA(25647, 66054, F256, 17) (dual of [66054, 66007, 18]-code) | [i] | ||
| 27 | Linear OA(25644, 66050, F256, 16) (dual of [66050, 66006, 17]-code) | [i] | ||
| 28 | Linear OA(25645, 66053, F256, 16) (dual of [66053, 66008, 17]-code) | [i] | ||
| 29 | Linear OA(25641, 66051, F256, 15) (dual of [66051, 66010, 16]-code) | [i] | ||
| 30 | Linear OA(25642, 66054, F256, 15) (dual of [66054, 66012, 16]-code) | [i] | ||
| 31 | Linear OA(25629, 66051, F256, 11) (dual of [66051, 66022, 12]-code) | [i] | ||
| 32 | Linear OA(25627, 66050, F256, 10) (dual of [66050, 66023, 11]-code) | [i] | ||