Information on Result #658019
Linear OA(25611, 257, F256, 11) (dual of [257, 246, 12]-code or 257-arc in PG(10,256)), using algebraic-geometric code AG(F, Q+121P) 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(1622, 514, F16, 11) (dual of [514, 492, 12]-code) | [i] | Trace Code | |
| 2 | OA(3218, 257, S32, 11) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6415, 257, S64, 11) | [i] | ||
| 4 | OA(12813, 257, S128, 11) | [i] | ||
| 5 | Linear OA(25634, 514, F256, 23) (dual of [514, 480, 24]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25635, 517, F256, 23) (dual of [517, 482, 24]-code) | [i] | ||
| 7 | Linear OA(25656, 65794, F256, 23) (dual of [65794, 65738, 24]-code) | [i] | ||
| 8 | Linear OA(25633, 514, F256, 22) (dual of [514, 481, 23]-code) | [i] | ||
| 9 | Linear OA(25634, 517, F256, 22) (dual of [517, 483, 23]-code) | [i] | ||
| 10 | Linear OA(25654, 65793, F256, 22) (dual of [65793, 65739, 23]-code) | [i] | ||
| 11 | Linear OA(25616, 514, F256, 11) (dual of [514, 498, 12]-code) | [i] | ||
| 12 | Linear OA(25656, 65795, F256, 23) (dual of [65795, 65739, 24]-code) | [i] | ||
| 13 | Linear OA(25657, 65799, F256, 23) (dual of [65799, 65742, 24]-code) | [i] | ||
| 14 | Linear OA(25659, 65805, F256, 23) (dual of [65805, 65746, 24]-code) | [i] | ||
| 15 | Linear OA(25654, 65795, F256, 22) (dual of [65795, 65741, 23]-code) | [i] | ||
| 16 | Linear OA(25635, 546, F256, 23) (dual of [546, 511, 24]-code) | [i] | ||
| 17 | Linear OA(25634, 546, F256, 22) (dual of [546, 512, 23]-code) | [i] | ||
| 18 | Linear OA(25629, 65792, F256, 11) (dual of [65792, 65763, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 19 | Linear OA(25614, 260, F256, 13) (dual of [260, 246, 14]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 20 | Linear OA(25612, 260, F256, 11) (dual of [260, 248, 12]-code) | [i] | ✔ | |
| 21 | Linear OA(25618, 264, F256, 15) (dual of [264, 246, 16]-code) | [i] | ✔ | |
| 22 | Linear OA(25614, 264, F256, 11) (dual of [264, 250, 12]-code) | [i] | ✔ | |
| 23 | Linear OA(25622, 268, F256, 17) (dual of [268, 246, 18]-code) | [i] | ✔ | |
| 24 | Linear OA(25616, 268, F256, 11) (dual of [268, 252, 12]-code) | [i] | ✔ | |
| 25 | Linear OA(25626, 272, F256, 19) (dual of [272, 246, 20]-code) | [i] | ✔ | |
| 26 | Linear OA(25630, 276, F256, 21) (dual of [276, 246, 22]-code) | [i] | ✔ | |
| 27 | Linear OA(25634, 280, F256, 23) (dual of [280, 246, 24]-code) | [i] | ✔ | |
| 28 | Linear OA(25638, 284, F256, 25) (dual of [284, 246, 26]-code) | [i] | ✔ | |
| 29 | Linear OA(25642, 288, F256, 27) (dual of [288, 246, 28]-code) | [i] | ✔ | |
| 30 | Linear OA(25646, 292, F256, 29) (dual of [292, 246, 30]-code) | [i] | ✔ | |
| 31 | Linear OA(25650, 296, F256, 31) (dual of [296, 246, 32]-code) | [i] | ✔ | |
| 32 | Linear OA(25654, 300, F256, 33) (dual of [300, 246, 34]-code) | [i] | ✔ | |
| 33 | Linear OA(25616, 262, F256, 14) (dual of [262, 246, 15]-code) | [i] | ✔ | |
| 34 | Linear OA(25613, 262, F256, 11) (dual of [262, 249, 12]-code) | [i] | ✔ | |
| 35 | Linear OA(25628, 274, F256, 20) (dual of [274, 246, 21]-code) | [i] | ✔ | |
| 36 | Linear OA(25640, 286, F256, 26) (dual of [286, 246, 27]-code) | [i] | ✔ | |
| 37 | Linear OA(25652, 298, F256, 32) (dual of [298, 246, 33]-code) | [i] | ✔ | |
| 38 | Linear OA(25620, 266, F256, 16) (dual of [266, 246, 17]-code) | [i] | ✔ | |
| 39 | Linear OA(25615, 266, F256, 11) (dual of [266, 251, 12]-code) | [i] | ✔ | |
| 40 | Linear OA(25663, 66051, F256, 23) (dual of [66051, 65988, 24]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 41 | Linear OA(25661, 66050, F256, 22) (dual of [66050, 65989, 23]-code) | [i] | ||