What is this space look like or what is the elements of this quotient space:
$\dfrac {\mathbb {F}_{q^k}}{V}$
Given that $V$ is the span of a number of unit vectors of length $k$. and $F_{q^k}~$ is the vector space composed of all $k$-tuples over the finite field $F_q$ (the finite field of q elements where $q$ is a prime power)
Quotient spaces are very easy for finite dimensional vector spaces. Let $V$ be a vector space of dimension $n$ over $F$, and $M$ a subspace of dimension $m$. Since finite dimensional vector spaces are completely characterized by the base field and by their dimension, $V/M \simeq F^{n - m}$.