Information on Result #661228
Linear OA(1692, 520, F16, 45) (dual of [520, 428, 46]-code), using trace code based on linear OA(25646, 260, F256, 45) (dual of [260, 214, 46]-code), using
- construction X applied to AG(F, Q+104P) ⊂ AG(F, Q+105P) [i] based on
- linear OA(25645, 257, F256, 45) (dual of [257, 212, 46]-code or 257-arc in PG(44,256)), using algebraic-geometric code AG(F, Q+104P) 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]
- linear OA(25643, 257, F256, 43) (dual of [257, 214, 44]-code or 257-arc in PG(42,256)), using algebraic-geometric code AG(F, Q+105P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(1693, 521, F16, 45) (dual of [521, 428, 46]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(16123, 591, F16, 45) (dual of [591, 468, 46]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(16124, 593, F16, 45) (dual of [593, 469, 46]-code) | [i] | ||
| 4 | Linear OA(16125, 595, F16, 45) (dual of [595, 470, 46]-code) | [i] | ||
| 5 | Linear OOA(1692, 260, F16, 2, 45) (dual of [(260, 2), 428, 46]-NRT-code) | [i] | OOA Folding | |