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- Joel E. Iiams
- J. Comb. Theory, Ser. A
- 1995

For an integer b ≥ 2 and for x ∈ [0, 1), define ρ b (x) = ∞ n=0 {{b n x}} b n , where {{t}} denotes the fractional part of the real number t. A number of properties of ρ b are derived, and then a connection between ρ b and the rumor conjecture is established. To form a rumor sequence {z n }, first select integers b ≥ 2 and k ≥ 1. Then select an integer z 0… (More)

Rumor sequences are generated recursively as follows: fix nonnegative integers b, c, and let z 0 = 0. For n ≥ 1, define z n = (bz n−1 + c) mod n, where the least nonnegative residue modulo n is taken. There have been a few papers dealing with the behavior of rumor sequences, but they all concern that behavior when the value of c is fixed. It turns out that… (More)

Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Hadamard difference sets. In the abelian case, a group of order 2 2 tq2 has a difference set if and only if the exponent of the group is less tq 2 Ž than or equal to 2. In a previous work R. the authors constructed a difference set in a nonabelian… (More)

- Joel E. Iiams
- Des. Codes Cryptography
- 2001

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