Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of $x^{q^k}+\cdots+x^{q}+x=a$ in $GF{2^n}$   Though it is well known that the roots of any affine polynomial over a finite
field can be computed by a system of linear equations by using a normal base of
the field, such solving approach appears to be difficult to apply when the
field is fairly large. Thus, it may be of great interest to find an explicit
representation of the solutions independently of the field base. This was
previously done only for quadratic equations over a binary finite field. This
paper gives an explicit representation of solutions for a much wider class of
affine polynomials over a binary prime field.

37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin