Information on Result #671617
Linear OA(25664, 517, F256, 42) (dual of [517, 453, 43]-code), using (u, u+v)-construction based on
- linear OA(25621, 257, F256, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using
- extended Reed–Solomon code RSe(236,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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]
- algebraic-geometric code AG(F, Q+77P) with degQ = 4 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,47P) with degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25643, 260, F256, 42) (dual of [260, 217, 43]-code), using
- construction X applied to AG(F,107P) ⊂ AG(F,108P) [i] based on
- linear OA(25642, 257, F256, 42) (dual of [257, 215, 43]-code or 257-arc in PG(41,256)), using algebraic-geometric code AG(F,107P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25640, 257, F256, 40) (dual of [257, 217, 41]-code or 257-arc in PG(39,256)), using algebraic-geometric code AG(F,108P) 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), 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,107P) ⊂ AG(F,108P) [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(12874, 517, S128, 42) | [i] | Discarding Parts of the Base for OAs | |