Information on Result #661411
Linear OA(16130, 572, F16, 51) (dual of [572, 442, 52]-code), using trace code based on linear OA(25665, 286, F256, 51) (dual of [286, 221, 52]-code), using
- construction X applied to AG(F, Q+67P) ⊂ AG(F, Q+72P) [i] based on
- linear OA(25651, 257, F256, 51) (dual of [257, 206, 52]-code or 257-arc in PG(50,256)), using algebraic-geometric code AG(F, Q+101P) 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(25636, 257, F256, 36) (dual of [257, 221, 37]-code or 257-arc in PG(35,256)), using algebraic-geometric code AG(F,110P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25614, 29, F256, 14) (dual of [29, 15, 15]-code or 29-arc in PG(13,256)), using
- discarding factors / shortening the dual code based on linear OA(25614, 256, F256, 14) (dual of [256, 242, 15]-code or 256-arc in PG(13,256)), using
- Reed–Solomon code RS(242,256) [i]
- discarding factors / shortening the dual code based on linear OA(25614, 256, F256, 14) (dual of [256, 242, 15]-code or 256-arc in PG(13,256)), 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 OOA(16130, 286, F16, 2, 51) (dual of [(286, 2), 442, 52]-NRT-code) | [i] | OOA Folding | |