Information on Result #658010
Linear OA(25622, 260, F256, 21) (dual of [260, 238, 22]-code), using construction X applied to AG(F, Q+116P) ⊂ AG(F, Q+117P) based on
- linear OA(25621, 257, F256, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using algebraic-geometric code AG(F, Q+116P) 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(25619, 257, F256, 19) (dual of [257, 238, 20]-code or 257-arc in PG(18,256)), using algebraic-geometric code AG(F, Q+117P) 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(488, 1040, F4, 21) (dual of [1040, 952, 22]-code) | [i] | Trace Code | |
| 2 | Linear OA(1644, 520, F16, 21) (dual of [520, 476, 22]-code) | [i] | ||
| 3 | OA(3236, 260, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6430, 260, S64, 21) | [i] | ||
| 5 | OA(12826, 260, S128, 21) | [i] | ||
| 6 | Linear OA(25666, 520, F256, 43) (dual of [520, 454, 44]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25667, 522, F256, 43) (dual of [522, 455, 44]-code) | [i] | ||
| 8 | Linear OA(25665, 520, F256, 42) (dual of [520, 455, 43]-code) | [i] | ||
| 9 | Linear OA(25666, 522, F256, 42) (dual of [522, 456, 43]-code) | [i] | ||
| 10 | Linear OA(25632, 517, F256, 21) (dual of [517, 485, 22]-code) | [i] | ||
| 11 | Linear OA(25633, 520, F256, 21) (dual of [520, 487, 22]-code) | [i] | ||