Information on Result #1805856
Digital (10, 16, 19686)-net over F27, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(2716, 19686, F27, 6) (dual of [19686, 19670, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2716, 19683, F27, 6) (dual of [19683, 19667, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2713, 19683, F27, 5) (dual of [19683, 19670, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 | (18, 24, 19686)-net in base 9 | [i] | Base Change | |