Information on Result #736037
Linear OA(25631, 65795, F256, 13) (dual of [65795, 65764, 14]-code), using (u, u+v)-construction based on
- linear OA(2566, 257, F256, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using
- extended Reed–Solomon code RSe(251,256) [i]
- algebraic-geometric code AG(F,125P) with 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+82P) 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,50P) with degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25625, 65538, F256, 13) (dual of [65538, 65513, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [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(12836, 65795, S128, 13) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25631, 65795, F256, 2, 13) (dual of [(65795, 2), 131559, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25631, 65795, F256, 3, 13) (dual of [(65795, 3), 197354, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(25631, 65795, F256, 4, 13) (dual of [(65795, 4), 263149, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(25631, 65795, F256, 5, 13) (dual of [(65795, 5), 328944, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(25631, 65795, F256, 6, 13) (dual of [(65795, 6), 394739, 14]-NRT-code) | [i] | ||
| 7 | Digital (18, 31, 65795)-net over F256 | [i] | ||
| 8 | Linear OOA(25631, 13159, F256, 5, 13) (dual of [(13159, 5), 65764, 14]-NRT-code) | [i] | OOA Folding | |