Information on Result #629189
Linear OA(1642, 514, F16, 21) (dual of [514, 472, 22]-code), using trace code based on linear OA(25621, 257, F256, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using
- extended Reed–Solomon code RSe(236,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+116P) 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+77P) 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,47P) 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(1643, 515, F16, 21) (dual of [515, 472, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1653, 538, F16, 21) (dual of [538, 485, 22]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1654, 547, F16, 21) (dual of [547, 493, 22]-code) | [i] | ||
| 4 | Linear OA(1655, 552, F16, 21) (dual of [552, 497, 22]-code) | [i] | ||
| 5 | Linear OA(1656, 559, F16, 21) (dual of [559, 503, 22]-code) | [i] | ||
| 6 | Linear OA(1651, 671, F16, 21) (dual of [671, 620, 22]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(1652, 760, F16, 21) (dual of [760, 708, 22]-code) | [i] | ||
| 8 | Linear OA(1653, 870, F16, 21) (dual of [870, 817, 22]-code) | [i] | ||
| 9 | Linear OOA(1642, 257, F16, 2, 21) (dual of [(257, 2), 472, 22]-NRT-code) | [i] | OOA Folding | |