Self-inversive polynomials, curves, and codes
David Joyner, Tony Shaska · Contemporary mathematics - American Mathematical Society · 2018
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 X \mathcal {X} is a superelliptic curve defined over C \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 ) y^n = f(x) or y n = x f ( x ) y^n = x f(x) , where f ( x ) 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.