Information on Result #657999
Linear OA(25631, 257, F256, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using algebraic-geometric code AG(F, Q+111P) 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(1662, 514, F16, 31) (dual of [514, 452, 32]-code) | [i] | Trace Code | |
| 2 | OA(3250, 257, S32, 31) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6442, 257, S64, 31) | [i] | ||
| 4 | OA(12836, 257, S128, 31) | [i] | ||
| 5 | Linear OA(25646, 514, F256, 31) (dual of [514, 468, 32]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25634, 260, F256, 33) (dual of [260, 226, 34]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 7 | Linear OA(25632, 260, F256, 31) (dual of [260, 228, 32]-code) | [i] | ✔ | |
| 8 | Linear OA(25638, 264, F256, 35) (dual of [264, 226, 36]-code) | [i] | ✔ | |
| 9 | Linear OA(25634, 264, F256, 31) (dual of [264, 230, 32]-code) | [i] | ✔ | |
| 10 | Linear OA(25642, 268, F256, 37) (dual of [268, 226, 38]-code) | [i] | ✔ | |
| 11 | Linear OA(25636, 268, F256, 31) (dual of [268, 232, 32]-code) | [i] | ✔ | |
| 12 | Linear OA(25646, 272, F256, 39) (dual of [272, 226, 40]-code) | [i] | ✔ | |
| 13 | Linear OA(25638, 272, F256, 31) (dual of [272, 234, 32]-code) | [i] | ✔ | |
| 14 | Linear OA(25650, 276, F256, 41) (dual of [276, 226, 42]-code) | [i] | ✔ | |
| 15 | Linear OA(25640, 276, F256, 31) (dual of [276, 236, 32]-code) | [i] | ✔ | |
| 16 | Linear OA(25654, 280, F256, 43) (dual of [280, 226, 44]-code) | [i] | ✔ | |
| 17 | Linear OA(25642, 280, F256, 31) (dual of [280, 238, 32]-code) | [i] | ✔ | |
| 18 | Linear OA(25658, 284, F256, 45) (dual of [284, 226, 46]-code) | [i] | ✔ | |
| 19 | Linear OA(25644, 284, F256, 31) (dual of [284, 240, 32]-code) | [i] | ✔ | |
| 20 | Linear OA(25662, 288, F256, 47) (dual of [288, 226, 48]-code) | [i] | ✔ | |
| 21 | Linear OA(25646, 288, F256, 31) (dual of [288, 242, 32]-code) | [i] | ✔ | |
| 22 | Linear OA(25666, 292, F256, 49) (dual of [292, 226, 50]-code) | [i] | ✔ | |
| 23 | Linear OA(25648, 292, F256, 31) (dual of [292, 244, 32]-code) | [i] | ✔ | |
| 24 | Linear OA(25650, 296, F256, 31) (dual of [296, 246, 32]-code) | [i] | ✔ | |
| 25 | Linear OA(25636, 262, F256, 34) (dual of [262, 226, 35]-code) | [i] | ✔ | |
| 26 | Linear OA(25633, 262, F256, 31) (dual of [262, 229, 32]-code) | [i] | ✔ | |
| 27 | Linear OA(25648, 274, F256, 40) (dual of [274, 226, 41]-code) | [i] | ✔ | |
| 28 | Linear OA(25639, 274, F256, 31) (dual of [274, 235, 32]-code) | [i] | ✔ | |
| 29 | Linear OA(25660, 286, F256, 46) (dual of [286, 226, 47]-code) | [i] | ✔ | |
| 30 | Linear OA(25645, 286, F256, 31) (dual of [286, 241, 32]-code) | [i] | ✔ | |
| 31 | Linear OA(25640, 266, F256, 36) (dual of [266, 226, 37]-code) | [i] | ✔ | |
| 32 | Linear OA(25635, 266, F256, 31) (dual of [266, 231, 32]-code) | [i] | ✔ | |