Information on Result #629164
Linear OA(1612, 514, F16, 6) (dual of [514, 502, 7]-code), using trace code based on linear OA(2566, 257, F256, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using
- extended Reed–Solomon code RSe(251,256) [i]
- algebraic-geometric code AG(F,125P) 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]
- algebraic-geometric code AG(F, Q+82P) with degQ = 4 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,50P) with 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(1613, 515, F16, 6) (dual of [515, 502, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1613, 516, F16, 6) (dual of [516, 503, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(1612, 257, F16, 2, 6) (dual of [(257, 2), 502, 7]-NRT-code) | [i] | OOA Folding | |