Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-inversive polynomials, curves, and codes   We study connections between self-inversive and self-reciprocal polynomials,
reduction theory of binary forms, minimal models of curves, and formally
self-dual codes. We prove that if $\mathcal X$ is a superelliptic curve defined
over $\mathbb C$ and its reduced automorphism group is nontrivial or not
isomorphic to a cyclic group, then we can write its equation as $y^n = f(x)$ or
$y^n = x f(x)$, where $f(x)$ is a self-inversive or self-reciprocal polynomial.
Moreover, we state a conjecture on the coefficients of the zeta polynomial of
extremal formally self-dual codes.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn