Information on Result #735988
Linear OA(25644, 65795, F256, 18) (dual of [65795, 65751, 19]-code), using (u, u+v)-construction based on
- linear OA(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using
- extended Reed–Solomon code RSe(248,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+122P) 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+81P) 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+49P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [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(12851, 65795, S128, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25644, 65795, F256, 2, 18) (dual of [(65795, 2), 131546, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25644, 65795, F256, 3, 18) (dual of [(65795, 3), 197341, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(25644, 65795, F256, 4, 18) (dual of [(65795, 4), 263136, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(25644, 65795, F256, 5, 18) (dual of [(65795, 5), 328931, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(25644, 65795, F256, 6, 18) (dual of [(65795, 6), 394726, 19]-NRT-code) | [i] | ||
| 7 | Digital (26, 44, 65795)-net over F256 | [i] | ||
| 8 | Linear OOA(25644, 32897, F256, 2, 18) (dual of [(32897, 2), 65750, 19]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25644, 13159, F256, 5, 18) (dual of [(13159, 5), 65751, 19]-NRT-code) | [i] | ||