In the present paper we obtain new upper bound estimates for the number of solutions of the congruence x ≡ yr (mod p); x, y ∈ N, x, y ≤ H, r ∈ U , for certain ranges of H and |U|, where U is a subset of the field of residue classes modulo p having small multiplicative doubling. We then use this estimate to show that the number of solutions of the congruence x ≡ λ (mod p); x ∈ N, L < x < L+ p/n,...

We propose a convolutional encoder over the finite ring of integers modulo pk ,Zpk , where p is a prime number and k is any positive integer, to generate a space-time convolutional code (STCC). Under this structure, we prove three properties related to the generator matrix of the convolutional code that can be used to simplify the code search procedure for STCCs over Zpk . Some STCCs of large d...

The motivation for computing in a suitably chosen homomorphic image of the original problem domain is that the computation there is either easier or is possible, whereas in the original domain it was either harder or impossible. For example, any homomorphic image of the infinite ring of integers is a finite ring, and computation in a finite set is usually easier than in an infinite set; as we h...