Information on Result #671560
Linear OA(25663, 66056, F256, 22) (dual of [66056, 65993, 23]-code), using (u, u−v, u+v+w)-construction based on
- linear OA(2568, 260, F256, 7) (dual of [260, 252, 8]-code), using
- construction X applied to AG(F, Q+123P) ⊂ AG(F, Q+124P) [i] based on
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using 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]
- linear OA(2565, 257, F256, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using algebraic-geometric code AG(F, Q+124P) 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+123P) ⊂ AG(F, Q+124P) [i] based on
- linear OA(25612, 260, F256, 11) (dual of [260, 248, 12]-code), using
- construction X applied to AG(F, Q+121P) ⊂ AG(F, Q+122P) [i] based on
- 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(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using 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 (see above)
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code) (see above)
- construction X applied to AG(F, Q+121P) ⊂ AG(F, Q+122P) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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
None.