Information on Result #736023
Linear OA(25638, 65800, F256, 15) (dual of [65800, 65762, 16]-code), using (u, u+v)-construction based on
- linear OA(2569, 262, F256, 7) (dual of [262, 253, 8]-code), using
- construction X applied to AG(F,83P) ⊂ AG(F,84P) [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(2564, 257, F256, 4) (dual of [257, 253, 5]-code or 257-arc in PG(3,256)), using 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 (see above)
- linear OA(2562, 5, F256, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to AG(F,83P) ⊂ AG(F,84P) [i] based on
- linear OA(25629, 65538, F256, 15) (dual of [65538, 65509, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(14) ⊂ Ce(13) [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(25638, 13160, F256, 5, 15) (dual of [(13160, 5), 65762, 16]-NRT-code) | [i] | OOA Folding | |