Information on Result #664847
Linear OA(1694, 581, F16, 35) (dual of [581, 487, 36]-code), using (u, u+v)-construction based on
- linear OA(1624, 67, F16, 17) (dual of [67, 43, 18]-code), using
- construction X applied to AG(F,46P) ⊂ AG(F,48P) [i] based on
- linear OA(1623, 64, F16, 17) (dual of [64, 41, 18]-code), using algebraic-geometric code AG(F,46P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1623, 64, F16, 17) (dual of [64, 41, 18]-code), using algebraic-geometric code AG(F,46P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,46P) ⊂ AG(F,48P) [i] based on
- linear OA(1670, 514, F16, 35) (dual of [514, 444, 36]-code), using
- trace code [i] based on linear OA(25635, 257, F256, 35) (dual of [257, 222, 36]-code or 257-arc in PG(34,256)), using
- extended Reed–Solomon code RSe(222,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+109P) 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+73P) with degQ = 2 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, Q+43P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- trace code [i] based on linear OA(25635, 257, F256, 35) (dual of [257, 222, 36]-code or 257-arc in PG(34,256)), using
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 OOA(1694, 290, F16, 2, 35) (dual of [(290, 2), 486, 36]-NRT-code) | [i] | OOA Folding | |