Information on Result #657761
Linear OA(25613, 260, F256, 12) (dual of [260, 247, 13]-code), using construction X applied to AG(F,122P) ⊂ AG(F,123P) based on
- 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 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- linear OA(25610, 257, F256, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using algebraic-geometric code AG(F,123P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(452, 1040, F4, 12) (dual of [1040, 988, 13]-code) | [i] | Trace Code | |
| 2 | Linear OA(1626, 520, F16, 12) (dual of [520, 494, 13]-code) | [i] | ||
| 3 | OA(3221, 260, S32, 12) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6418, 260, S64, 12) | [i] | ||
| 5 | OA(12815, 260, S128, 12) | [i] | ||
| 6 | Linear OA(25639, 520, F256, 25) (dual of [520, 481, 26]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25640, 522, F256, 25) (dual of [522, 482, 26]-code) | [i] | ||
| 8 | Linear OA(25662, 65797, F256, 25) (dual of [65797, 65735, 26]-code) | [i] | ||
| 9 | Linear OA(25638, 520, F256, 24) (dual of [520, 482, 25]-code) | [i] | ||
| 10 | Linear OA(25639, 522, F256, 24) (dual of [522, 483, 25]-code) | [i] | ||
| 11 | Linear OA(25660, 65796, F256, 24) (dual of [65796, 65736, 25]-code) | [i] | ||
| 12 | Linear OA(25619, 517, F256, 12) (dual of [517, 498, 13]-code) | [i] | ||
| 13 | Linear OA(25662, 65798, F256, 25) (dual of [65798, 65736, 26]-code) | [i] | ||
| 14 | Linear OA(25663, 65802, F256, 25) (dual of [65802, 65739, 26]-code) | [i] | ||
| 15 | Linear OA(25665, 65808, F256, 25) (dual of [65808, 65743, 26]-code) | [i] | ||
| 16 | Linear OA(25660, 65798, F256, 24) (dual of [65798, 65738, 25]-code) | [i] | ||
| 17 | Linear OA(25661, 65801, F256, 24) (dual of [65801, 65740, 25]-code) | [i] | ||
| 18 | Linear OA(25662, 65804, F256, 24) (dual of [65804, 65742, 25]-code) | [i] | ||
| 19 | Linear OA(25663, 65807, F256, 24) (dual of [65807, 65744, 25]-code) | [i] | ||
| 20 | Linear OA(25664, 65810, F256, 24) (dual of [65810, 65746, 25]-code) | [i] | ||
| 21 | Linear OA(25668, 66053, F256, 24) (dual of [66053, 65985, 25]-code) | [i] | (u, u−v, u+v+w)-Construction | |