Information on Result #671668
Linear OA(25653, 520, F256, 34) (dual of [520, 467, 35]-code), using (u, u+v)-construction based on
- linear OA(25618, 260, F256, 17) (dual of [260, 242, 18]-code), using
- construction X applied to AG(F, Q+118P) ⊂ AG(F, Q+119P) [i] based on
- linear OA(25617, 257, F256, 17) (dual of [257, 240, 18]-code or 257-arc in PG(16,256)), using algebraic-geometric code AG(F, Q+118P) 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(25615, 257, F256, 15) (dual of [257, 242, 16]-code or 257-arc in PG(14,256)), using algebraic-geometric code AG(F, Q+119P) 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
- construction X applied to AG(F, Q+118P) ⊂ AG(F, Q+119P) [i] based on
- linear OA(25635, 260, F256, 34) (dual of [260, 225, 35]-code), using
- construction X applied to AG(F,111P) ⊂ AG(F,112P) [i] based on
- linear OA(25634, 257, F256, 34) (dual of [257, 223, 35]-code or 257-arc in PG(33,256)), using algebraic-geometric code AG(F,111P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25632, 257, F256, 32) (dual of [257, 225, 33]-code or 257-arc in PG(31,256)), using algebraic-geometric code AG(F,112P) with 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) (see above)
- construction X applied to AG(F,111P) ⊂ AG(F,112P) [i] based on
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 | OA(12861, 520, S128, 34) | [i] | Discarding Parts of the Base for OAs | |