Information on Result #629196
Linear OA(1650, 514, F16, 25) (dual of [514, 464, 26]-code), using trace code based on linear OA(25625, 257, F256, 25) (dual of [257, 232, 26]-code or 257-arc in PG(24,256)), using
- extended Reed–Solomon code RSe(232,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+114P) 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,77P) 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+45P) with degQ = 6 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(1651, 515, F16, 25) (dual of [515, 464, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1664, 547, F16, 25) (dual of [547, 483, 26]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1665, 552, F16, 25) (dual of [552, 487, 26]-code) | [i] | ||
| 4 | Linear OA(1666, 559, F16, 25) (dual of [559, 493, 26]-code) | [i] | ||
| 5 | Linear OA(1667, 563, F16, 25) (dual of [563, 496, 26]-code) | [i] | ||
| 6 | Linear OA(1668, 579, F16, 25) (dual of [579, 511, 26]-code) | [i] | ||
| 7 | Linear OA(1660, 685, F16, 25) (dual of [685, 625, 26]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(1661, 764, F16, 25) (dual of [764, 703, 26]-code) | [i] | ||
| 9 | Linear OOA(1650, 257, F16, 2, 25) (dual of [(257, 2), 464, 26]-NRT-code) | [i] | OOA Folding | |