Information on Result #661365
Linear OA(16122, 568, F16, 48) (dual of [568, 446, 49]-code), using trace code based on linear OA(25661, 284, F256, 48) (dual of [284, 223, 49]-code), using
- construction X applied to AG(F,104P) ⊂ AG(F,111P) [i] based on
- linear OA(25648, 257, F256, 48) (dual of [257, 209, 49]-code or 257-arc in PG(47,256)), using algebraic-geometric code AG(F,104P) 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(25634, 257, F256, 34) (dual of [257, 223, 35]-code or 257-arc in PG(33,256)), using algebraic-geometric code AG(F,111P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25613, 27, F256, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,256)), using
- discarding factors / shortening the dual code based on linear OA(25613, 256, F256, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), using
- Reed–Solomon code RS(243,256) [i]
- discarding factors / shortening the dual code based on linear OA(25613, 256, F256, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), 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(16123, 569, F16, 48) (dual of [569, 446, 49]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16122, 284, F16, 2, 48) (dual of [(284, 2), 446, 49]-NRT-code) | [i] | OOA Folding | |