Information on Result #735970
Linear OA(25653, 65805, F256, 20) (dual of [65805, 65752, 21]-code), using (u, u+v)-construction based on
- linear OA(25613, 264, F256, 10) (dual of [264, 251, 11]-code), using
- construction X applied to AG(F,123P) ⊂ AG(F,125P) [i] based on
- linear OA(25610, 257, F256, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using algebraic-geometric code AG(F,123P) 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]
- linear OA(2566, 257, F256, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using algebraic-geometric code AG(F,125P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2563, 7, F256, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,256) or 7-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to AG(F,123P) ⊂ AG(F,125P) [i] based on
- linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(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, using
- construction X applied to Ce(19) ⊂ Ce(17) [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(25653, 21935, F256, 3, 20) (dual of [(21935, 3), 65752, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(25653, 13161, F256, 5, 20) (dual of [(13161, 5), 65752, 21]-NRT-code) | [i] | ||