Information on Result #1313636
Linear OA(1634, 919, F16, 13) (dual of [919, 885, 14]-code), using 397 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 10 times 0, 1, 27 times 0, 1, 62 times 0, 1, 116 times 0, 1, 174 times 0) based on linear OA(1626, 514, F16, 13) (dual of [514, 488, 14]-code), using
- trace code [i] 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: 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(1634, 919, F16, 2, 13) (dual of [(919, 2), 1804, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (21, 34, 919)-net over F16 | [i] | ||