A note on the crosscorrelation of maximal length FCSR sequences
Designs, Codes and Cryptography
Distribution properties of compressing sequences derived from primitive sequences over Z/(pe)
IEEE Transactions on Information Theory
A class of injective compressing maps on linear recurring sequences over a Galois ring
Problems of Information Transmission
On the distinctness of decimations of generalized l-sequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
On the distinctness of maximal length sequences over Z/(pq) modulo 2
Finite Fields and Their Applications
The nonlinear complexity of level sequences over Z/(4)
Finite Fields and Their Applications
A new result on the distinctness of primitive sequences over Z/ (pq) modulo 2
Finite Fields and Their Applications
Periods of termwise exclusive ors of maximal length FCSR sequences
Finite Fields and Their Applications
On the distinctness of modular reductions of primitive sequences modulo square-free odd integers
Information Processing Letters
On the distinctness of modular reductions of primitive sequences over Z/(232-1)
Designs, Codes and Cryptography
| Hi-index | 754.90 |
Let Z/(pe) be the integer residue ring with odd prime p≥5 and integer e≥2. For a sequence a_ over Z/(pe), there is a unique p-adic expansion a_=a_0+a_·p+...+a_e-1·pe-1, where each a_i is a sequence over {0,1,...,p-1}, and can be regarded as a sequence over the finite field GF(p) naturally. Let f(x) be a primitive polynomial over Z/(pe), and G'(f(x),pe) the set of all primitive sequences generated by f(x) over Z/(pe). Set φe-1 (x0,...,xe-1) = xe-1k + ηe-2,1(x0, x1,...,xe-2) ψe-1(x0,...,xe-1) = xe-1k + ηe-2,2(x0,x1,...,xe-2) where ηe-2,1 and ηe-2,2 are arbitrary functions of e-1 variables over GF(p) and 2≤k≤p-1. Then the compression mapping φe-1:{G'(f(x),pe) → GF(p)∞ a_ → φe-1(a_0,...,a_e-1) is injective, that is, a_ = b_ if and only if φe-1(a_0,...,a_e-1) = φe-1(b_0,...,b_e-1) for a_,b_ ∈ G'(f(x),pe). Furthermore, if f(x) is a strongly primitive polynomial over Z/(pe), then φe-1(a_0,...,a_e-1) = ψe-1(b_0,...,b_e-1) if and only if a_ = b_ and φe-1(x0,...,xe-1) = ψe-1(x0,...,xe-1) for a_,b_ ∈ G'(f(x),pe).