Information on Result #1188080
Digital (30, 35, 390629)-net over F5, using net defined by OOA based on linear OOA(535, 390629, F5, 5, 5) (dual of [(390629, 5), 1953110, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(535, 781259, F5, 5) (dual of [781259, 781224, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(534, 781258, F5, 5) (dual of [781258, 781224, 6]-code), using
- trace code [i] based on linear OA(2517, 390629, F25, 5) (dual of [390629, 390612, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(2517, 390625, F25, 5) (dual of [390625, 390608, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 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
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(2517, 390629, F25, 5) (dual of [390629, 390612, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(534, 781258, F5, 5) (dual of [781258, 781224, 6]-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 (117, 127, 3746069)-net over F5 | [i] | (u, u+v)-Construction for Nets | |