On the Distinctness of Binary Sequences Derived From Primitive Sequences Modulo Square-Free Odd Integers
Qun-Xiong Zheng, Wen‐Feng Qi, Tian Tian · IEEE Transactions on Information Theory · 2012
LetMbe a square-free odd integer andZ/(M) the integer residue ring moduloM. This paper studies the distinctness of primitive sequences overZ/(M) modulo 2. Recently, for the case ofM=pq, a product of two distinct prime numberspandq, the problem has been almost completely solved. As for the case thatMis a product of more prime numbers, the problem has been quite resistant to proof. In this paper, a partial proof is given by showing that a class of primitive sequences of order 2n'+1 overZ/(M) is distinct modulo 2, wheren'is a positive integer. Besides as an independent interest, this paper also involves two distribution properties of primitive sequences overZ/(M), which are related closely to our main results.