Information on Result #658017
Linear OA(25613, 257, F256, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using algebraic-geometric code AG(F, Q+120P) 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(1626, 514, F16, 13) (dual of [514, 488, 14]-code) | [i] | Trace Code | |
| 2 | OA(3221, 257, S32, 13) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6418, 257, S64, 13) | [i] | ||
| 4 | OA(12815, 257, S128, 13) | [i] | ||
| 5 | Linear OA(25640, 514, F256, 27) (dual of [514, 474, 28]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25641, 517, F256, 27) (dual of [517, 476, 28]-code) | [i] | ||
| 7 | Linear OA(25666, 65794, F256, 27) (dual of [65794, 65728, 28]-code) | [i] | ||
| 8 | Linear OA(25639, 514, F256, 26) (dual of [514, 475, 27]-code) | [i] | ||
| 9 | Linear OA(25640, 517, F256, 26) (dual of [517, 477, 27]-code) | [i] | ||
| 10 | Linear OA(25664, 65793, F256, 26) (dual of [65793, 65729, 27]-code) | [i] | ||
| 11 | Linear OA(25619, 514, F256, 13) (dual of [514, 495, 14]-code) | [i] | ||
| 12 | Linear OA(25666, 65795, F256, 27) (dual of [65795, 65729, 28]-code) | [i] | ||
| 13 | Linear OA(25667, 65799, F256, 27) (dual of [65799, 65732, 28]-code) | [i] | ||
| 14 | Linear OA(25664, 65795, F256, 26) (dual of [65795, 65731, 27]-code) | [i] | ||
| 15 | Linear OA(25641, 546, F256, 27) (dual of [546, 505, 28]-code) | [i] | ||
| 16 | Linear OA(25640, 546, F256, 26) (dual of [546, 506, 27]-code) | [i] | ||
| 17 | Linear OA(25616, 260, F256, 15) (dual of [260, 244, 16]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 18 | Linear OA(25614, 260, F256, 13) (dual of [260, 246, 14]-code) | [i] | ✔ | |
| 19 | Linear OA(25620, 264, F256, 17) (dual of [264, 244, 18]-code) | [i] | ✔ | |
| 20 | Linear OA(25616, 264, F256, 13) (dual of [264, 248, 14]-code) | [i] | ✔ | |
| 21 | Linear OA(25624, 268, F256, 19) (dual of [268, 244, 20]-code) | [i] | ✔ | |
| 22 | Linear OA(25618, 268, F256, 13) (dual of [268, 250, 14]-code) | [i] | ✔ | |
| 23 | Linear OA(25628, 272, F256, 21) (dual of [272, 244, 22]-code) | [i] | ✔ | |
| 24 | Linear OA(25620, 272, F256, 13) (dual of [272, 252, 14]-code) | [i] | ✔ | |
| 25 | Linear OA(25632, 276, F256, 23) (dual of [276, 244, 24]-code) | [i] | ✔ | |
| 26 | Linear OA(25636, 280, F256, 25) (dual of [280, 244, 26]-code) | [i] | ✔ | |
| 27 | Linear OA(25640, 284, F256, 27) (dual of [284, 244, 28]-code) | [i] | ✔ | |
| 28 | Linear OA(25644, 288, F256, 29) (dual of [288, 244, 30]-code) | [i] | ✔ | |
| 29 | Linear OA(25648, 292, F256, 31) (dual of [292, 244, 32]-code) | [i] | ✔ | |
| 30 | Linear OA(25652, 296, F256, 33) (dual of [296, 244, 34]-code) | [i] | ✔ | |
| 31 | Linear OA(25656, 300, F256, 35) (dual of [300, 244, 36]-code) | [i] | ✔ | |
| 32 | Linear OA(25660, 304, F256, 37) (dual of [304, 244, 38]-code) | [i] | ✔ | |
| 33 | Linear OA(25664, 308, F256, 39) (dual of [308, 244, 40]-code) | [i] | ✔ | |
| 34 | Linear OA(25618, 262, F256, 16) (dual of [262, 244, 17]-code) | [i] | ✔ | |
| 35 | Linear OA(25615, 262, F256, 13) (dual of [262, 247, 14]-code) | [i] | ✔ | |
| 36 | Linear OA(25630, 274, F256, 22) (dual of [274, 244, 23]-code) | [i] | ✔ | |
| 37 | Linear OA(25642, 286, F256, 28) (dual of [286, 244, 29]-code) | [i] | ✔ | |
| 38 | Linear OA(25654, 298, F256, 34) (dual of [298, 244, 35]-code) | [i] | ✔ | |
| 39 | Linear OA(25622, 266, F256, 18) (dual of [266, 244, 19]-code) | [i] | ✔ | |
| 40 | Linear OA(25617, 266, F256, 13) (dual of [266, 249, 14]-code) | [i] | ✔ | |
| 41 | Linear OA(25662, 306, F256, 38) (dual of [306, 244, 39]-code) | [i] | ✔ | |