  We study the finite field extension estimates for Hamming varieties $H_j,
j\in \mathbb F_q^*,$ defined by $H_j=\{x\in \mathbb F_q^d: \prod_{k=1}^d
x_k=j\},$ where $\mathbb F_q^d$ denotes the $d$-dimensional vector space over a
finite field $\mathbb F_q$ with $q$ elements. We show that although the maximal
Fourier decay bound on $H_j$ away from the origin is not good, the Stein-Tomas
$L^2\to L^r$ extension estimate for $H_j$ holds.
