Information on Result #693093
Linear OA(2586, 390652, F25, 21) (dual of [390652, 390566, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,7]) based on
- linear OA(2581, 390626, F25, 21) (dual of [390626, 390545, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2557, 390626, F25, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [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, using the rational function field F25(x) [i]
- 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 OOA(2586, 390652, F25, 2, 21) (dual of [(390652, 2), 781218, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (65, 86, 390652)-net over F25 | [i] | ||
| 3 | Linear OOA(2586, 195326, F25, 2, 21) (dual of [(195326, 2), 390566, 22]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2586, 39065, F25, 21, 21) (dual of [(39065, 21), 820279, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |