Character sums on an oriented singer conic and explicit Ramanujan double covers

Pin-Chi Hung, Ming-Hsuan Kang

Let $q$ be odd. The trace conic in ${\mathbb{F}}_{q^3}$ determines a Singer difference set in ${\mathbb{F}}_{q^3}^{\times }/{\mathbb{F}}_q^{\times }$ and a natural square-class lift to $\mat…