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 maximal length sequences over Z/(pq) modulo 2
Finite Fields and Their Applications
A new result on the distinctness of primitive sequences over Z/ (pq) modulo 2
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 be the integer residue ring with odd prime and integer . For a sequence over , there is an unique -adic expansion , where each is a sequence over , and can be regarded as a sequence over the prime field GF naturally. Let be a strongly primitive polynomial over , and the set of all primitive sequences generated by over . Suppose that GF GF . It is shown that any function in is an injective map from to GF, and the derived sequences of different functions are also different. That is, if and only if and for and . These injective functions in can be considered as good candidates for the keys of a stream cipher.