Further Results on the Distinctness of Binary Sequences Derived From Primitive Sequences Modulo Square-Free Odd Integers
Qun-Xiong Zheng, Wen‐Feng Qi · IEEE Transactions on Information Theory · 2013
This paper studies the distinctness of primitive sequences overZ/(M) modulo 2, whereMis an odd integer that is composite and square-free, andZ/(M) is the integer residue ring moduloM. A new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomialf(x) overZ/(M) are pairwise distinct modulo 2. Such result improves a recent result obtained in our previous paper, and consequently, the set of primitive sequences overZ/(M) that can be proven to be distinct modulo 2 is greatly enlarged.