Further Results on the Distinctness of Binary Sequences Derived From Primitive Sequences Modulo Square-Free Odd Integers

Abstract

This paper studies the distinctness of primitive sequences over Z/(M) modulo 2, where M is an odd integer that is composite and square-free, and Z/(M) is the integer residue ring modulo M. A new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f(x) over Z/(M) are pairwise distinct modulo 2. Such result improves a recent result obtained in our previous paper, and consequently, the set of primitive sequences over Z/(M) that can be proven to be distinct modulo 2 is greatly enlarged.