Minimal degree liftings in characteristic 2

In this paper we analyze liftings of hyperelliptic curves over perfect fields in characteristic 2 to curves over rings of Witt vectors. This theory can be applied to construct error-correcting codes; lifts of points with minimal degrees are likely to yield the best codes, and these are the main focus of the paper. We find upper and lower bounds for their degrees, give conditions to achieve the lower bounds and analyze the existence of lifts of the Frobenius. Finally, we exhibit explicit computations for genus 2 and show codes obtained using this theory.