Information on Result #1179444
Digital (15, 19, 7815)-net over F5, using net defined by OOA based on linear OOA(519, 7815, F5, 4, 4) (dual of [(7815, 4), 31241, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(519, 7815, F5, 3, 4) (dual of [(7815, 3), 23426, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(519, 15630, F5, 4) (dual of [15630, 15611, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(519, 15631, F5, 4) (dual of [15631, 15612, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(519, 15625, F5, 4) (dual of [15625, 15606, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(513, 15625, F5, 3) (dual of [15625, 15612, 4]-code or 15625-cap in PG(12,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(519, 15631, F5, 4) (dual of [15631, 15612, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(519, 15630, F5, 4) (dual of [15630, 15611, 5]-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 (83, 91, 4202115)-net over F5 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (92, 101, 4202115)-net over F5 | [i] | ||