The Gauss sums and Jacobi sums over Galois ring GR( p, r).

Galois rings and exponential sums over Galois rings have many applications in algebraic combinatorics, coding theory and cryptography. In this paper, we present explicit description on the Gauss sums and Jacobi sums over Galois ring GR( p, r), and show that the values of these sums can be reduced to the Gauss sums and Jacobi sums over finite field $$\mathbb{F}_{p^r }$$ for all non-trivial cases. [ABSTRACT FROM AUTHOR]