Information on Result #658055
Linear OA(25614, 264, F256, 11) (dual of [264, 250, 12]-code), using construction X applied to AG(F, Q+121P) ⊂ AG(F, Q+123P) based on
- linear OA(25611, 257, F256, 11) (dual of [257, 246, 12]-code or 257-arc in PG(10,256)), using algebraic-geometric code AG(F, Q+121P) 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(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 (see above)
- linear OA(2563, 7, F256, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,256) or 7-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), 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(1628, 528, F16, 11) (dual of [528, 500, 12]-code) | [i] | Trace Code | |
| 2 | OA(12816, 264, S128, 11) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(25659, 65801, F256, 23) (dual of [65801, 65742, 24]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(25657, 65800, F256, 22) (dual of [65800, 65743, 23]-code) | [i] | ||
| 5 | Linear OA(25659, 65802, F256, 23) (dual of [65802, 65743, 24]-code) | [i] | ||
| 6 | Linear OA(25660, 65806, F256, 23) (dual of [65806, 65746, 24]-code) | [i] | ||
| 7 | Linear OA(25657, 65802, F256, 22) (dual of [65802, 65745, 23]-code) | [i] | ||
| 8 | Linear OA(25658, 65805, F256, 22) (dual of [65805, 65747, 23]-code) | [i] | ||