What does this notation mean?

Question

I am currently completing a Combinatorics homework and came across this question:

"A $q$-ary $[n, k, d]$ code is a subset $C$ of $\mathbb{F}^n_q$ ..."

What is the set $\mathbb{F}^n_q$?

Answer 1

$\mathbb{F}_q$ is the field with $q$ elements.
$q$ will be the power of a prime $q=p^k$. $\mathbb{F}_q$ can be thought of as polynomials of degree less than $k$, with coefficients in $\mathbb{Z}_p$ (integers modulo $p$);
where the polynomials are modulo $g(x)$ for some polynomial $g(x)$. $g(x)$ is irreducible and has degree $k$.
$\mathbb{F}_q^n$ is then vectors $(f_1,f_2,\ldots,f_n)$ where each $f_i$ is in the field $\mathbb{F}_q$.