Information on Result #1188064
Digital (22, 27, 15628)-net over F5, using net defined by OOA based on linear OOA(527, 15628, F5, 5, 5) (dual of [(15628, 5), 78113, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(527, 31257, F5, 5) (dual of [31257, 31230, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(526, 31256, F5, 5) (dual of [31256, 31230, 6]-code), using
- trace code [i] based on linear OA(2513, 15628, F25, 5) (dual of [15628, 15615, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(2513, 15625, F25, 5) (dual of [15625, 15612, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2510, 15625, F25, 4) (dual of [15625, 15615, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 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(2513, 15628, F25, 5) (dual of [15628, 15615, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(526, 31256, F5, 5) (dual of [31256, 31230, 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 (109, 119, 3371068)-net over F5 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (118, 129, 3371068)-net over F5 | [i] | ||