Information on Result #657760
Linear OA(25612, 257, F256, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using algebraic-geometric code AG(F,122P) 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(448, 1028, F4, 12) (dual of [1028, 980, 13]-code) | [i] | Trace Code | |
| 2 | Linear OA(1624, 514, F16, 12) (dual of [514, 490, 13]-code) | [i] | ||
| 3 | Linear OA(1623, 257, F16, 12) (dual of [257, 234, 13]-code) | [i] | Base Reduction for Projective Spaces | |
| 4 | OA(3220, 257, S32, 12) | [i] | Discarding Parts of the Base for OAs | |
| 5 | OA(6416, 257, S64, 12) | [i] | ||
| 6 | OA(12814, 257, S128, 12) | [i] | ||
| 7 | Linear OA(25637, 514, F256, 25) (dual of [514, 477, 26]-code) | [i] | (u, u+v)-Construction | |
| 8 | Linear OA(25638, 517, F256, 25) (dual of [517, 479, 26]-code) | [i] | ||
| 9 | Linear OA(25661, 65794, F256, 25) (dual of [65794, 65733, 26]-code) | [i] | ||
| 10 | Linear OA(25636, 514, F256, 24) (dual of [514, 478, 25]-code) | [i] | ||
| 11 | Linear OA(25637, 517, F256, 24) (dual of [517, 480, 25]-code) | [i] | ||
| 12 | Linear OA(25659, 65793, F256, 24) (dual of [65793, 65734, 25]-code) | [i] | ||
| 13 | Linear OA(25618, 514, F256, 12) (dual of [514, 496, 13]-code) | [i] | ||
| 14 | Linear OA(25661, 65795, F256, 25) (dual of [65795, 65734, 26]-code) | [i] | ||
| 15 | Linear OA(25662, 65799, F256, 25) (dual of [65799, 65737, 26]-code) | [i] | ||
| 16 | Linear OA(25664, 65805, F256, 25) (dual of [65805, 65741, 26]-code) | [i] | ||
| 17 | Linear OA(25666, 65811, F256, 25) (dual of [65811, 65745, 26]-code) | [i] | ||
| 18 | Linear OA(25659, 65795, F256, 24) (dual of [65795, 65736, 25]-code) | [i] | ||
| 19 | Linear OA(25638, 546, F256, 25) (dual of [546, 508, 26]-code) | [i] | ||
| 20 | Linear OA(25637, 546, F256, 24) (dual of [546, 509, 25]-code) | [i] | ||
| 21 | Linear OA(25615, 260, F256, 14) (dual of [260, 245, 15]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 22 | Linear OA(25613, 260, F256, 12) (dual of [260, 247, 13]-code) | [i] | ✔ | |
| 23 | Linear OA(25619, 264, F256, 16) (dual of [264, 245, 17]-code) | [i] | ✔ | |
| 24 | Linear OA(25615, 264, F256, 12) (dual of [264, 249, 13]-code) | [i] | ✔ | |
| 25 | Linear OA(25623, 268, F256, 18) (dual of [268, 245, 19]-code) | [i] | ✔ | |
| 26 | Linear OA(25617, 268, F256, 12) (dual of [268, 251, 13]-code) | [i] | ✔ | |
| 27 | Linear OA(25627, 272, F256, 20) (dual of [272, 245, 21]-code) | [i] | ✔ | |
| 28 | Linear OA(25619, 272, F256, 12) (dual of [272, 253, 13]-code) | [i] | ✔ | |
| 29 | Linear OA(25631, 276, F256, 22) (dual of [276, 245, 23]-code) | [i] | ✔ | |
| 30 | Linear OA(25635, 280, F256, 24) (dual of [280, 245, 25]-code) | [i] | ✔ | |
| 31 | Linear OA(25639, 284, F256, 26) (dual of [284, 245, 27]-code) | [i] | ✔ | |
| 32 | Linear OA(25643, 288, F256, 28) (dual of [288, 245, 29]-code) | [i] | ✔ | |
| 33 | Linear OA(25647, 292, F256, 30) (dual of [292, 245, 31]-code) | [i] | ✔ | |
| 34 | Linear OA(25651, 296, F256, 32) (dual of [296, 245, 33]-code) | [i] | ✔ | |
| 35 | Linear OA(25655, 300, F256, 34) (dual of [300, 245, 35]-code) | [i] | ✔ | |
| 36 | Linear OA(25659, 304, F256, 36) (dual of [304, 245, 37]-code) | [i] | ✔ | |
| 37 | Linear OA(25617, 262, F256, 15) (dual of [262, 245, 16]-code) | [i] | ✔ | |
| 38 | Linear OA(25614, 262, F256, 12) (dual of [262, 248, 13]-code) | [i] | ✔ | |
| 39 | Linear OA(25629, 274, F256, 21) (dual of [274, 245, 22]-code) | [i] | ✔ | |
| 40 | Linear OA(25641, 286, F256, 27) (dual of [286, 245, 28]-code) | [i] | ✔ | |
| 41 | Linear OA(25653, 298, F256, 33) (dual of [298, 245, 34]-code) | [i] | ✔ | |
| 42 | Linear OA(25621, 266, F256, 17) (dual of [266, 245, 18]-code) | [i] | ✔ | |
| 43 | Linear OA(25616, 266, F256, 12) (dual of [266, 250, 13]-code) | [i] | ✔ | |
| 44 | Linear OA(25667, 66050, F256, 24) (dual of [66050, 65983, 25]-code) | [i] | (u, u−v, u+v+w)-Construction | |