EXPANSIONS OF ELEMENTS WRITTEN WITH RESPECT TO A QUADRATIC GENERATING POLYNOMIAL

Abstract

Let p(x, y) = y2 + b1y − b0 ∈ Fq[x, y], where Fq is a finite field of

q elements; b1, b0 ∈ Fq[x] and let R := Fq[x, y]/ (p(x, y)). A Scheicher

Thuswaldner algorithm enables us to represent each element of R through

a digit system. All possible representations of elements in R are deter

mined when deg b1 ≤ deg b0. As for the case deg b1 > deg b0, the same

analysis is carried out subject to an assumption on the existence of a

unique maximal term