The $p$-powers dividing certain exponential sums

We define the notion of couple density $(D,\mathbf{b})$ where $D$ is a non-empty subset of ${\mathbb{Z}}^m$ and $\mathbf{b}$ a fixed element in $\{0,\cdots ,q-2{\}}^m;$ We determine a minimum in terms of the density of the couple $(D,\mathbf{b})$ for the $q$-adic valuation of the sum $S_{\mathrm{\ell }}(F,\mathbf{b})$ with $F$ a Laurent polynomial. And we show that this minimum is a bound for the $q$-adic valuation of the zeros and poles of the associated $L$-function.