Information on Result #671620
Linear OA(25667, 524, F256, 42) (dual of [524, 457, 43]-code), using (u, u+v)-construction based on
- linear OA(25623, 262, F256, 21) (dual of [262, 239, 22]-code), using
- construction X applied to AG(F, Q+77P) ⊂ AG(F, Q+78P) [i] based on
- linear OA(25621, 257, F256, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using algebraic-geometric code AG(F, Q+116P) 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(25618, 257, F256, 18) (dual of [257, 239, 19]-code or 257-arc in PG(17,256)), using algebraic-geometric code AG(F,119P) 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
- linear OA(25644, 262, F256, 42) (dual of [262, 218, 43]-code), using
- construction X applied to AG(F, Q+70P) ⊂ AG(F, Q+71P) [i] based on
- linear OA(25642, 257, F256, 42) (dual of [257, 215, 43]-code or 257-arc in PG(41,256)), using algebraic-geometric code AG(F,107P) with degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25639, 257, F256, 39) (dual of [257, 218, 40]-code or 257-arc in PG(38,256)), using algebraic-geometric code AG(F, Q+107P) 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)) (see above)
- construction X applied to AG(F, Q+70P) ⊂ AG(F, Q+71P) [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(12877, 524, S128, 42) | [i] | Discarding Parts of the Base for OAs | |