arXiv subjects

Caleb Shor

Publications and source records attributed to Caleb Shor.

2 recordsLinked to original sources

arXiv2014

On Jacobians of curves with superelliptic components

We investigate the decomposition of Jacobians of superelliptic curves based on their automorphisms. For curve with equation $y^n=f(x^m)$ we provide an necessary and sufficient condition in terms of $m$ and $n$ for the decomposition of the Jacobian induced by the automorphisms of the curve. Moreover, we generalize a construction in \cite{Ya} of a family of non-hyperelliptic curves $\mathcal X_{r,s} $ and determine arithmetic conditions on $r$ and $s$ that the Jacobians $\mbox{Jac} (\mathcal X_{r, s})$ decomposes.

math.AG↗

arXiv2013

Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields

In this paper we continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over rings of characteristic $p=2$ and $p=5$ which have the same theta functions. We also look at a generalization of codes over imaginary quadratic fields, providing examples of non-equivalent pairs with the same theta function for $p=3$ and $p=5$.

math.NT↗