Information on Result #661384
Linear OA(16124, 528, F16, 59) (dual of [528, 404, 60]-code), using trace code based on linear OA(25662, 264, F256, 59) (dual of [264, 202, 60]-code), using
- construction X applied to AG(F, Q+97P) ⊂ AG(F, Q+99P) [i] based on
- linear OA(25659, 257, F256, 59) (dual of [257, 198, 60]-code or 257-arc in PG(58,256)), using algebraic-geometric code AG(F, Q+97P) 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(25655, 257, F256, 55) (dual of [257, 202, 56]-code or 257-arc in PG(54,256)), using algebraic-geometric code AG(F, Q+99P) 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(16125, 529, F16, 59) (dual of [529, 404, 60]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16124, 264, F16, 2, 59) (dual of [(264, 2), 404, 60]-NRT-code) | [i] | OOA Folding | |