Information on Result #671626
Linear OA(25665, 524, F256, 41) (dual of [524, 459, 42]-code), using (u, u+v)-construction based on
- linear OA(25622, 262, F256, 20) (dual of [262, 240, 21]-code), using
- construction X applied to AG(F, Q+78P) ⊂ AG(F, Q+79P) [i] based on
- 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, using the rational function field F256(x) [i]
- linear OA(25617, 257, F256, 17) (dual of [257, 240, 18]-code or 257-arc in PG(16,256)), using algebraic-geometric code AG(F, Q+118P) 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(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+78P) ⊂ AG(F, Q+79P) [i] based on
- linear OA(25643, 262, F256, 41) (dual of [262, 219, 42]-code), using
- construction X applied to AG(F, Q+71P) ⊂ AG(F, Q+72P) [i] based on
- linear OA(25641, 257, F256, 41) (dual of [257, 216, 42]-code or 257-arc in PG(40,256)), using algebraic-geometric code AG(F, Q+106P) 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(25638, 257, F256, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) 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)) (see above)
- construction X applied to AG(F, Q+71P) ⊂ AG(F, Q+72P) [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(12875, 524, S128, 41) | [i] | Discarding Parts of the Base for OAs | |