Minimal Degree Liftings of Edwards Curves

Voloch and Walker used liftings of elliptic curves to create error-correcting codes, for which lifting of points with smaller degrees for their coordinate functions give better parameters. Thus, one might be interested in constructing liftings with minimal possible degrees. Here we study liftings of twisted Edwards curve with minimal degrees. We prove that up to the second coordinate these minimal degrees are given by the canonical lifting and elliptic Teichmüller lift, give upper and lower bounds for the degrees of Edwards lifts, and prove that the lower bound can be achieved for the third coordinate.