  The Fibonacci cube of dimension n, denoted as $\Gamma$ n , is the subgraph of
the n-cube 5 Q n induced by vertices with no consecutive 1's. Ashrafi and his
co-authors proved the non-existence of perfect codes in $\Gamma$ n for n $\ge$
4. As an open problem the authors suggest to consider the existence of perfect
codes in generalizations of Fibonacci cubes. The most direct generalization is
the family $\Gamma$ n (1 s) of subgraphs induced by strings without 1 s as a
substring where s $\ge$ 2 is a given integer. In a precedent work 10 we proved
the existence of a perfect code in $\Gamma$ n (1 s) for n = 2 p -- 1 and s
$\ge$ 3.2 p--2 for any integer p $\ge$ 2. The Lucas cube $\Lambda$ n is
obtained from $\Gamma$ n by removing vertices that start and end with 1. Very
often the same problems are studied on Fibonacci cubes and Lucas cube. In this
note we prove the non-existence of perfect codes in $\Lambda$ n for n $\ge$ 4
and 15 prove the existence of perfect codes in some generalized Lucas cube
$\Lambda$ n (1 s).
