Information on Result #658024
Linear OA(2568, 260, F256, 7) (dual of [260, 252, 8]-code), using construction X applied to AG(F, Q+123P) ⊂ AG(F, Q+124P) based on
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using algebraic-geometric code AG(F, Q+123P) with degQ = 3 and 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(2565, 257, F256, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using algebraic-geometric code AG(F, Q+124P) with degQ = 3 and 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(1616, 520, F16, 7) (dual of [520, 504, 8]-code) | [i] | Trace Code | |
| 2 | OA(6411, 260, S64, 7) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(12810, 260, S128, 7) | [i] | ||
| 4 | Linear OA(25624, 520, F256, 15) (dual of [520, 496, 16]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(25637, 65797, F256, 15) (dual of [65797, 65760, 16]-code) | [i] | ||
| 6 | Linear OA(25635, 65796, F256, 14) (dual of [65796, 65761, 15]-code) | [i] | ||
| 7 | Linear OA(25637, 65798, F256, 15) (dual of [65798, 65761, 16]-code) | [i] | ||
| 8 | Linear OA(25638, 65802, F256, 15) (dual of [65802, 65764, 16]-code) | [i] | ||
| 9 | Linear OA(25635, 65798, F256, 14) (dual of [65798, 65763, 15]-code) | [i] | ||
| 10 | Linear OA(25636, 65801, F256, 14) (dual of [65801, 65765, 15]-code) | [i] | ||
| 11 | Linear OA(25617, 65796, F256, 7) (dual of [65796, 65779, 8]-code) | [i] | Generalized (u, u+v)-Construction | |
| 12 | Linear OA(25618, 66050, F256, 7) (dual of [66050, 66032, 8]-code) | [i] | ||
| 13 | Linear OA(25665, 66057, F256, 23) (dual of [66057, 65992, 24]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 14 | Linear OA(25666, 66059, F256, 23) (dual of [66059, 65993, 24]-code) | [i] | ||
| 15 | Linear OA(25663, 66056, F256, 22) (dual of [66056, 65993, 23]-code) | [i] | ||
| 16 | Linear OA(25660, 66057, F256, 21) (dual of [66057, 65997, 22]-code) | [i] | ||
| 17 | Linear OA(25642, 66054, F256, 15) (dual of [66054, 66012, 16]-code) | [i] | ||
| 18 | Linear OA(25639, 66053, F256, 14) (dual of [66053, 66014, 15]-code) | [i] | ||