I‑AIMS Institute for Artificial Intelligence
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Self-inversive polynomials, curves, and codes

David Joyner, Tanush Shaska

I-AIMS paper 2016-2 · Published in Contemp. Math. 703 (2018), 189–208 · 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 is a superelliptic curve defined over ℂ and its reduced automorphism group is nontrivial or not isomorphic to a cyclic group, then we can write its equation as yⁿ = f(x) or yⁿ = 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.

MSC classes: 14Hxx, 11Gxx

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