Information on Result #735864
Linear OA(25668, 65802, F256, 27) (dual of [65802, 65734, 28]-code), using (u, u+v)-construction based on
- linear OA(25614, 260, F256, 13) (dual of [260, 246, 14]-code), using
- construction X applied to AG(F, Q+120P) ⊂ AG(F, Q+121P) [i] based on
- linear OA(25613, 257, F256, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using algebraic-geometric code AG(F, Q+120P) 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]
- linear OA(25611, 257, F256, 11) (dual of [257, 246, 12]-code or 257-arc in PG(10,256)), using algebraic-geometric code AG(F, Q+121P) with degQ = 3 and 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, Q+120P) ⊂ AG(F, Q+121P) [i] based on
- linear OA(25654, 65542, F256, 27) (dual of [65542, 65488, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 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 (see above)
- construction X applied to C([0,13]) ⊂ C([0,12]) [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(12878, 65802, S128, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25668, 32901, F256, 2, 27) (dual of [(32901, 2), 65734, 28]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(25668, 21934, F256, 3, 27) (dual of [(21934, 3), 65734, 28]-NRT-code) | [i] | ||