Information on Result #629224
Linear OA(1686, 514, F16, 43) (dual of [514, 428, 44]-code), using trace code based on linear OA(25643, 257, F256, 43) (dual of [257, 214, 44]-code or 257-arc in PG(42,256)), using
- extended Reed–Solomon code RSe(214,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+105P) 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,71P) with 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+42P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
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(1687, 515, F16, 43) (dual of [515, 428, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1686, 257, F16, 2, 43) (dual of [(257, 2), 428, 44]-NRT-code) | [i] | OOA Folding | |