Cyclotomic construction of $\lambda$-fold near-factorizations of cyclic groups

Abstract

The study of near-factorizations of finite groups dates back to the 1950s. Recently, this topic has attracted renewed attention, and the concept has been extended to $\lambda$-fold near-factorizations, in which each non-identity group element appears exactly $\lambda \ge 1$ times. This paper presents a cyclotomic construction of $\lambda$-fold near-factorizations in the cyclic group $\mathbb{F}_p$, where $p = 4n^4 + 12n^2 + 1$ is prime for $n \ge 1$.