Spectral properties of generalized Paley graphs and their associated irreducible cyclic codes

Ricardo A. Podestá, Denis E. Videla

For $q=p^m$ with $p$ prime and $k\mid q-1$, we consider the generalized Paley graph $\Gamma (k,q)=Cay({\mathbb{F}}_q,R_k)$, with $R_k=\{x^k:x\in {\mathbb{F}}_q^{\ast }\}$, and the irreduci…