Information on Result #665200
Linear OA(1643, 538, F16, 17) (dual of [538, 495, 18]-code), using (u, u+v)-construction based on
- linear OA(169, 24, F16, 8) (dual of [24, 15, 9]-code), using
- extended algebraic-geometric code AGe(F,15P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- linear OA(1634, 514, F16, 17) (dual of [514, 480, 18]-code), using
- trace code [i] based on linear OA(25617, 257, F256, 17) (dual of [257, 240, 18]-code or 257-arc in PG(16,256)), using
- extended Reed–Solomon code RSe(240,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+118P) 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]
- algebraic-geometric code AG(F, Q+79P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+47P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- trace code [i] based on linear OA(25617, 257, F256, 17) (dual of [257, 240, 18]-code or 257-arc in PG(16,256)), 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(1643, 269, F16, 2, 17) (dual of [(269, 2), 495, 18]-NRT-code) | [i] | OOA Folding | |