Information on Result #1185862
Digital (47, 54, 349533)-net over F4, using net defined by OOA based on linear OOA(454, 349533, F4, 7, 7) (dual of [(349533, 7), 2446677, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(454, 1048600, F4, 7) (dual of [1048600, 1048546, 8]-code), using
- 2 times code embedding in larger space [i] based on linear OA(452, 1048598, F4, 7) (dual of [1048598, 1048546, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(451, 1048576, F4, 7) (dual of [1048576, 1048525, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(421, 22, F4, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
- dual of repetition code with length 22 [i]
- linear OA(41, 22, F4, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(452, 1048598, F4, 7) (dual of [1048598, 1048546, 8]-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 (200, 214, 5143017)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (211, 226, 5143017)-net over F4 | [i] | ||