Information on Result #658009
Linear OA(25621, 257, F256, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using algebraic-geometric code AG(F, Q+116P) 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(1642, 514, F16, 21) (dual of [514, 472, 22]-code) | [i] | Trace Code | |
| 2 | OA(3234, 257, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6428, 257, S64, 21) | [i] | ||
| 4 | OA(12824, 257, S128, 21) | [i] | ||
| 5 | Linear OA(25664, 514, F256, 43) (dual of [514, 450, 44]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25665, 517, F256, 43) (dual of [517, 452, 44]-code) | [i] | ||
| 7 | Linear OA(25663, 514, F256, 42) (dual of [514, 451, 43]-code) | [i] | ||
| 8 | Linear OA(25664, 517, F256, 42) (dual of [517, 453, 43]-code) | [i] | ||
| 9 | Linear OA(25631, 514, F256, 21) (dual of [514, 483, 22]-code) | [i] | ||
| 10 | Linear OA(25665, 546, F256, 43) (dual of [546, 481, 44]-code) | [i] | ||
| 11 | Linear OA(25664, 546, F256, 42) (dual of [546, 482, 43]-code) | [i] | ||
| 12 | Linear OA(25624, 260, F256, 23) (dual of [260, 236, 24]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 13 | Linear OA(25622, 260, F256, 21) (dual of [260, 238, 22]-code) | [i] | ✔ | |
| 14 | Linear OA(25628, 264, F256, 25) (dual of [264, 236, 26]-code) | [i] | ✔ | |
| 15 | Linear OA(25624, 264, F256, 21) (dual of [264, 240, 22]-code) | [i] | ✔ | |
| 16 | Linear OA(25632, 268, F256, 27) (dual of [268, 236, 28]-code) | [i] | ✔ | |
| 17 | Linear OA(25626, 268, F256, 21) (dual of [268, 242, 22]-code) | [i] | ✔ | |
| 18 | Linear OA(25636, 272, F256, 29) (dual of [272, 236, 30]-code) | [i] | ✔ | |
| 19 | Linear OA(25628, 272, F256, 21) (dual of [272, 244, 22]-code) | [i] | ✔ | |
| 20 | Linear OA(25640, 276, F256, 31) (dual of [276, 236, 32]-code) | [i] | ✔ | |
| 21 | Linear OA(25630, 276, F256, 21) (dual of [276, 246, 22]-code) | [i] | ✔ | |
| 22 | Linear OA(25644, 280, F256, 33) (dual of [280, 236, 34]-code) | [i] | ✔ | |
| 23 | Linear OA(25632, 280, F256, 21) (dual of [280, 248, 22]-code) | [i] | ✔ | |
| 24 | Linear OA(25648, 284, F256, 35) (dual of [284, 236, 36]-code) | [i] | ✔ | |
| 25 | Linear OA(25634, 284, F256, 21) (dual of [284, 250, 22]-code) | [i] | ✔ | |
| 26 | Linear OA(25652, 288, F256, 37) (dual of [288, 236, 38]-code) | [i] | ✔ | |
| 27 | Linear OA(25656, 292, F256, 39) (dual of [292, 236, 40]-code) | [i] | ✔ | |
| 28 | Linear OA(25660, 296, F256, 41) (dual of [296, 236, 42]-code) | [i] | ✔ | |
| 29 | Linear OA(25664, 300, F256, 43) (dual of [300, 236, 44]-code) | [i] | ✔ | |
| 30 | Linear OA(25668, 304, F256, 45) (dual of [304, 236, 46]-code) | [i] | ✔ | |
| 31 | Linear OA(25626, 262, F256, 24) (dual of [262, 236, 25]-code) | [i] | ✔ | |
| 32 | Linear OA(25623, 262, F256, 21) (dual of [262, 239, 22]-code) | [i] | ✔ | |
| 33 | Linear OA(25638, 274, F256, 30) (dual of [274, 236, 31]-code) | [i] | ✔ | |
| 34 | Linear OA(25629, 274, F256, 21) (dual of [274, 245, 22]-code) | [i] | ✔ | |
| 35 | Linear OA(25650, 286, F256, 36) (dual of [286, 236, 37]-code) | [i] | ✔ | |
| 36 | Linear OA(25662, 298, F256, 42) (dual of [298, 236, 43]-code) | [i] | ✔ | |
| 37 | Linear OA(25630, 266, F256, 26) (dual of [266, 236, 27]-code) | [i] | ✔ | |
| 38 | Linear OA(25625, 266, F256, 21) (dual of [266, 241, 22]-code) | [i] | ✔ | |