Information on Result #658042
Linear OA(25640, 264, F256, 37) (dual of [264, 224, 38]-code), using construction X applied to AG(F, Q+108P) ⊂ AG(F, Q+110P) based on
- linear OA(25637, 257, F256, 37) (dual of [257, 220, 38]-code or 257-arc in PG(36,256)), using algebraic-geometric code AG(F, Q+108P) 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(25633, 257, F256, 33) (dual of [257, 224, 34]-code or 257-arc in PG(32,256)), using algebraic-geometric code AG(F, Q+110P) 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(4160, 1056, F4, 37) (dual of [1056, 896, 38]-code) | [i] | Trace Code | |
| 2 | Linear OA(1680, 528, F16, 37) (dual of [528, 448, 38]-code) | [i] | ||
| 3 | OA(3264, 264, S32, 37) | [i] | Discarding Parts of the Base for OAs | |
| 4 | Linear OA(25660, 526, F256, 37) (dual of [526, 466, 38]-code) | [i] | (u, u+v)-Construction | |