Simple Combinatorics in finite rings

Simple Combinatorics in finite rings

Let $g = [g_{1} g_{2} \dots g_{r}] \in \Bbb Z_{q}^{r}$ be a given vector.
How many vectors $a = [a_{1} a_{2} \dots a_{r}] \in \Bbb Z_{q}^{r}$ are
such that:
$(1)$ $a^{T}g = 0$?
$(2)$ $a^{T}g = 1$?
$(3)$ $a^{T}g = q-1$?