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

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 $n\ge 1$.