Trace Representation of r-Ary Sequences Derived from Euler Quotients Modulo 2p

Abstract

We introduce the r-ary sequence with period 2p² derived from Euler quotients modulo 2p (p is an odd prime) where r is an odd prime divisor of (p-1). Then based on the cyclotomic theory and the theory of trace function in finite fields, we give the trace representation of the proposed sequence by determining the corresponding defining polynomial. Our results will be help for the implementation and the pseudo-random properties analysis of the sequences.