What does $^t$ mean in $x={}^t(x_1,x_2,…,x_n)$

Question

I'm reading this paper and came across some notation I don't know and which is pretty difficult to search for. The relevant section is the first paragraph of section 2.1 in the paper, copied below:

Let $q$ be a power of prime and $k$ be a finite field of order $q$. For integers $n, m\ge1$, denoted by $f_1(x),f_2(x),…,f_m(x)$ quadratic polynomials of $x={}^t(x_1,x_2,…,x_n)$ over $k$.

Question: What is the meaning & name of the $^t$ notation before the brackets? It is not defined and is obviously not an exponent due to its placement. They use it in a similar fashion later in section 2.2:

$$
f_i(x_1,x_2,…,x_n)={}^txF_ix+ \text{(linear.)}
$$

where $F_1,…,F_m$ are $n×n$ matrices over $k$

Answer 1

It should be the transpose. It is an aesthetic notation.

Instead of writing a vector as column, you would write it as a row.

So $(1,2,3)^t=\begin{pmatrix}1\\2\\3\end{pmatrix}$