Trace representation of the binary pq2-periodic sequences derived from Euler quotients

Abstract

Given a binary sequence, its trace representation allows us to reconstruct itself efficiently and to analyze its properties, such as the linear complexity. In this paper, we study a family of the binary sequences derived from Euler quotients modulo pq , where p and q are two distinct odd primes and p divides q −\u20091. Our main contribution is to give a trace representation of this family within these assumptions by determining the defining pairs of the corresponding subsequences. As a byproduct, we rediscover some known results of linear complexities by using trace representations of the proposed sequences.