lee weight and generalized lee weight for codes over ‎$‎‎z_{2^n}$

‎‎‎‎‎‎let $‎mathbb{z}_m$ be the ring of integers modulo $m$ in which $m=2^n$ for arbitrary $n$‎. ‎in this paper‎, ‎we will obtain a relationship between $wt_l(x)‎, ‎wt_l(y)$ and $wt_l(x+y)$ for any $x‎, ‎y in ‎mathbb{z}_m$‎. ‎‎let ‎$‎‎d_r^l(c)$‎‎ ‎denote ‎the ‎‎$r‎‎$‎-th generalized lee weight for code $c$ in which ‎$‎‎c$ ‎is ‎a linear code of length $n$ over $‎mathbb{z}_4$‎. also, ‎suppose that $c_1$ and $ c_2$ are two codes over $‎mathbb{z}_4$ and $c$ denotes the $(u‎, ‎u+v)$-construction of them‎. ‎in this paper‎, we will obtain an upper bound for $d_r^l(c)$ for all $r$‎, ‎$1 leq r leq rank(c)$‎. in addition, ‎we will obtain $d_1^l(c)$ in terms of $d_1^l(c_1)$ and $d_1^l(c_2)$.