Information on Result #657797
Linear OA(25615, 264, F256, 12) (dual of [264, 249, 13]-code), using construction X applied to AG(F,122P) ⊂ AG(F,124P) 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(2568, 257, F256, 8) (dual of [257, 249, 9]-code or 257-arc in PG(7,256)), using algebraic-geometric code AG(F,124P) with 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(1630, 528, F16, 12) (dual of [528, 498, 13]-code) | [i] | Trace Code | |
| 2 | OA(6420, 264, S64, 12) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(25664, 65801, F256, 25) (dual of [65801, 65737, 26]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(25662, 65800, F256, 24) (dual of [65800, 65738, 25]-code) | [i] | ||
| 5 | Linear OA(25664, 65802, F256, 25) (dual of [65802, 65738, 26]-code) | [i] | ||
| 6 | Linear OA(25665, 65806, F256, 25) (dual of [65806, 65741, 26]-code) | [i] | ||
| 7 | Linear OA(25662, 65802, F256, 24) (dual of [65802, 65740, 25]-code) | [i] | ||
| 8 | Linear OA(25663, 65805, F256, 24) (dual of [65805, 65742, 25]-code) | [i] | ||
| 9 | Linear OA(25664, 65808, F256, 24) (dual of [65808, 65744, 25]-code) | [i] | ||