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 letR := Fq[x,y]/(p(x,y)). A ScheicherThuswaldner algorithm enables us to represent each element of R through a digit system. All possible representations of elements in R are determined when degb1 ≤ degb0. 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