Information on Result #671834
Linear OA(25636, 65794, F256, 15) (dual of [65794, 65758, 16]-code), using (u, u+v)-construction based on
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using
- extended Reed–Solomon code RSe(250,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+123P) 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,83P) 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, Q+49P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
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 OOA(25636, 32897, F256, 2, 15) (dual of [(32897, 2), 65758, 16]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(25636, 21931, F256, 3, 15) (dual of [(21931, 3), 65757, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(25636, 9399, F256, 15, 15) (dual of [(9399, 15), 140949, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |