Compressing Mappings on Primitive Sequences over Z/(2e) and Its Galois Extension,

Let f(x) be a strongly primitive polynomial of degree n over Z/(2e), η(x0,x1,…,xe−2) a Boolean function of e−1 variables and (x0,x1,…,xe−1)=xe−1+η(x0,x1,…,xe−2)G (f(x),Z/(2e)) denotes the set of all sequences over Z/(2e) generated by f(x), F2∞ the set of all sequences over the binary field F2, then the compressing mapping is injective, that is, for , G(f(x),Z/(2e)), = if and only if Φ( )=Φ( ), i.e., ( 0,…, e−1)= ( 0,…, e−1) mod 2. In the second part of the paper, we generalize the above result over the Galois rings.