Information on Result #671682
Linear OA(25646, 514, F256, 31) (dual of [514, 468, 32]-code), using (u, u+v)-construction based on
- linear OA(25615, 257, F256, 15) (dual of [257, 242, 16]-code or 257-arc in PG(14,256)), using
- extended Reed–Solomon code RSe(242,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- 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, using the rational function field F256(x) [i]
- algebraic-geometric code AG(F, Q+79P) 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, Q+47P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25631, 257, F256, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using
- extended Reed–Solomon code RSe(226,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+111P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F,75P) 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,45P) with 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 | OA(12853, 514, S128, 31) | [i] | Discarding Parts of the Base for OAs | |