Denis E. Videla

The spectral relation between irreducible cyclic codes and generalized Paley graphs

Let $p$ be a prime and $\mathbb{F}_q/\mathbb{F}_r$ a finite field extension with $q=p^m$ and $r=p^s$. For any $k\mid q-1$, we consider $r$-ary irreducible cyclic codes (ICC) of the form $C(k,q/r) = \{(Tr_{q/r}(\gamma \omega^{ik})_{i=0}^{n-1})\}_{\gamma \in \mathbb{F}_r}$, with $\omega$ a primitive element of $\mathbb{F...