Information on Result #629176
Linear OA(1626, 514, F16, 13) (dual of [514, 488, 14]-code), using trace code based on linear OA(25613, 257, F256, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using
- extended Reed–Solomon code RSe(244,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+120P) 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,81P) 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+48P) 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(1627, 515, F16, 13) (dual of [515, 488, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1632, 531, F16, 13) (dual of [531, 499, 14]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1633, 538, F16, 13) (dual of [538, 505, 14]-code) | [i] | ||
| 4 | Linear OA(1634, 547, F16, 13) (dual of [547, 513, 14]-code) | [i] | ||
| 5 | Linear OA(1635, 552, F16, 13) (dual of [552, 517, 14]-code) | [i] | ||
| 6 | Linear OA(1633, 743, F16, 13) (dual of [743, 710, 14]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(1634, 919, F16, 13) (dual of [919, 885, 14]-code) | [i] | ||
| 8 | Linear OA(1635, 1153, F16, 13) (dual of [1153, 1118, 14]-code) | [i] | ||
| 9 | Linear OOA(1626, 257, F16, 2, 13) (dual of [(257, 2), 488, 14]-NRT-code) | [i] | OOA Folding | |