Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Cyclic Codes from APN Functions   Cyclic codes, as linear block error-correcting codes in coding theory, play a
vital role and have wide applications. Ding in \cite{D} constructed a number of
classes of cyclic codes from almost perfect nonlinear (APN) functions and
planar functions over finite fields and presented ten open problems on cyclic
codes from highly nonlinear functions. In this paper, we consider two open
problems involving the inverse APN functions $f(x)=x^{q^m-2}$ and the Dobbertin
APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$. From the calculation of
linear spans and the minimal polynomials of two sequences generated by these
two classes of APN functions, the dimensions of the corresponding cyclic codes
are determined and lower bounds on the minimum weight of these cyclic codes are
presented. Actually, we present a framework for the minimal polynomial and
linear span of the sequence $s^{\infty}$ defined by $s_t=Tr((1+\alpha^t)^e)$,
where $\alpha$ is a primitive element in $GF(q)$. These techniques can also be
applied into other open problems in \cite{D}.

5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex