A Construction of Zero-Difference Functions
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A function f from group (A,+) to group (B,+) is a (|A|, |Im(f)|, S) zero-difference function, if S is the minimal set such that for every non-zero a ∈ A, |{x ∈ A | f(x+a)-f(x)=0}|∈ S. ZDFs have connections with many combinatorial objects such as constant composition codes, constant weight codes, difference systems of sets and frequency-hopping sequences. In this paper, a generic method to construct ZDFs on algebraic rings, is proposed. Then the generic method is used for the rings Z_p^k, where p is a prime number and k> 2 is a positive integer, and for some other special rings.
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