Information on Result #671745
Linear OA(25637, 522, F256, 23) (dual of [522, 485, 24]-code), using (u, u+v)-construction 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, using the rational function field F256(x) [i]
- 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), 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+121P) ⊂ AG(F, Q+122P) [i] based on
- linear OA(25625, 262, F256, 23) (dual of [262, 237, 24]-code), using
- construction X applied to AG(F, Q+77P) ⊂ AG(F, Q+78P) [i] based on
- linear OA(25623, 257, F256, 23) (dual of [257, 234, 24]-code or 257-arc in PG(22,256)), using algebraic-geometric code AG(F, Q+115P) 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(25620, 257, F256, 20) (dual of [257, 237, 21]-code or 257-arc in PG(19,256)), using algebraic-geometric code AG(F,118P) 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, Q+77P) ⊂ AG(F, Q+78P) [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(12843, 522, S128, 23) | [i] | Discarding Parts of the Base for OAs | |