Information on Result #1196704
Digital (44, 64, 1565)-net over F25, using net defined by OOA based on linear OOA(2564, 1565, F25, 20, 20) (dual of [(1565, 20), 31236, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2564, 15650, F25, 20) (dual of [15650, 15586, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2564, 15651, F25, 20) (dual of [15651, 15587, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(256, 26, F25, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using
- extended Reed–Solomon code RSe(20,25) [i]
- algebraic-geometric code AG(F, Q+8P) 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]
- algebraic-geometric code AG(F, Q+5P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2564, 15651, F25, 20) (dual of [15651, 15587, 21]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (45, 65, 1565)-net over F25 | [i] | Net Duplication | |