Information on Result #665375
Linear OA(2510, 650, F25, 5) (dual of [650, 640, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(250, 26, F25, 0) (dual of [26, 26, 1]-code) (see above)
- linear OA(251, 26, F25, 1) (dual of [26, 25, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(251, 26, F25, 1) (dual of [26, 25, 2]-code) (see above)
- linear OA(251, 26, F25, 1) (dual of [26, 25, 2]-code) (see above)
- linear OA(252, 26, F25, 2) (dual of [26, 24, 3]-code or 26-arc in PG(1,25)), using
- extended Reed–Solomon code RSe(24,25) [i]
- Hamming code H(2,25) [i]
- algebraic-geometric code AG(F, Q+10P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- extended Reed–Solomon code RSe(21,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- algebraic-geometric code AG(F, Q+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
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 OA(2516, 16250, F25, 5) (dual of [16250, 16234, 6]-code) | [i] | Generalized (u, u+v)-Construction | |