Information on Result #736003
Linear OA(25645, 66052, F256, 17) (dual of [66052, 66007, 18]-code), using (u, u+v)-construction based on
- linear OA(25612, 514, F256, 8) (dual of [514, 502, 9]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2564, 257, F256, 4) (dual of [257, 253, 5]-code or 257-arc in PG(3,256)), using
- extended Reed–Solomon code RSe(253,256) [i]
- algebraic-geometric code AG(F,126P) 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,84P) 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+50P) 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(2568, 257, F256, 8) (dual of [257, 249, 9]-code or 257-arc in PG(7,256)), using
- extended Reed–Solomon code RSe(249,256) [i]
- algebraic-geometric code AG(F,124P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+82P) with degQ = 2 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 = 3 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2564, 257, F256, 4) (dual of [257, 253, 5]-code or 257-arc in PG(3,256)), using
- (u, u+v)-construction [i] based on
- linear OA(25633, 65538, F256, 17) (dual of [65538, 65505, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 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(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(16) ⊂ Ce(15) [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 | Linear OOA(25645, 33026, F256, 2, 17) (dual of [(33026, 2), 66007, 18]-NRT-code) | [i] | OOA Folding | |