Information on Result #661185
Linear OA(1684, 552, F16, 33) (dual of [552, 468, 34]-code), using trace code based on linear OA(25642, 276, F256, 33) (dual of [276, 234, 34]-code), using
- construction X applied to AG(F, Q+110P) ⊂ AG(F, Q+115P) [i] based on
- 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, using the rational function field F256(x) [i]
- linear OA(25623, 257, F256, 23) (dual of [257, 234, 24]-code or 257-arc in PG(22,256)), using algebraic-geometric code AG(F, Q+115P) 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(2569, 19, F256, 9) (dual of [19, 10, 10]-code or 19-arc in PG(8,256)), using
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- Reed–Solomon code RS(247,256) [i]
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), 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(1685, 553, F16, 33) (dual of [553, 468, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1684, 276, F16, 2, 33) (dual of [(276, 2), 468, 34]-NRT-code) | [i] | OOA Folding | |