Trace Representation of r-Ary Sequences Derived from Euler Quotients Modulo 2p
Rayan Mohammed, Xiaoni Du, Wengang Jin, Yanzhong Sun · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2021
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.