Information on Result #661165
Linear OA(1678, 520, F16, 38) (dual of [520, 442, 39]-code), using trace code based on linear OA(25639, 260, F256, 38) (dual of [260, 221, 39]-code), using
- construction X applied to AG(F,109P) ⊂ AG(F,110P) [i] based on
- linear OA(25638, 257, F256, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) 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(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(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1679, 521, F16, 38) (dual of [521, 442, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1678, 260, F16, 2, 38) (dual of [(260, 2), 442, 39]-NRT-code) | [i] | OOA Folding | |