Publications
Papers are grouped by subject.
Difference Sets and related objects
Cyclic relative difference sets and circulant weighing matrices. Journal of Algebraic Combinatorics 63, article 24 (2026). arXiv
Modular Golomb rulers and almost difference sets. IEEE Transactions on Information Theory 71 (2025), 5737–5743. arXiv
Signed difference sets. Designs, Codes and Cryptography 91 (2023), 2107–2115. arXiv
On difference sets with small λ. Journal of Algebraic Combinatorics 55 (2022), 109–115. arXiv
New nonexistence results on circulant weighing matrices, with K. T. Arasu and Yiran Zhang. Cryptography and Communications 13 (2021), 775–789. arXiv
A survey of the multiplier conjecture, with Bernhard Schmidt. Designs, Codes and Cryptography 78 (2016), 221–236.
On the existence of cyclic difference sets with small parameters, with Leonard D. Baumert. In High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams (2004), 61–68.
Some restrictions on orders of abelian planar difference sets. Journal of Combinatorial Mathematics and Combinatorial Computing 29 (1999), 241–246.
The Prime Power Conjecture is true for n < 2,000,000. Electronic Journal of Combinatorics 1 (1994), R6.
Covering Designs
Coverings, with Douglas Stinson. In Handbook of Combinatorial Designs, second edition (2007), pp. 365–372.
Asymptotically optimal covering designs, with Greg Kuperberg, Oren Patashnik, and Joel Spencer. Journal of Combinatorial Theory, Series A 75 (1996), 270–280.
New constructions for covering designs, with Greg Kuperberg and Oren Patashnik. Journal of Combinatorial Designs 3 (1995), 269–284.
C(12,6,3)=15, with Oren Patashnik, John Petro, and Herb Taylor. Ars Combinatoria 40 (1995), 161–177.
Coding Theory
Optimal hash functions for approximate closest pairs on the n-cube, with Victor Miller and Peter Ostapenko. IEEE Transactions on Information Theory 56 (2010), 984–991. arXiv
Perfect single error-correcting codes in the Johnson scheme. IEEE Transactions on Information Theory 52 (2006), 4670–4672. arXiv
A remark on Plotkin’s bound, with Warwick de Launey. IEEE Transactions on Information Theory 47 (2001), 352–355.
Equidistant arithmetic codes and character sums. Journal of Number Theory 46 (1994), 323–333.
Perfect multiple error-correcting arithmetic codes. Mathematics of Computation 49 (1987), 621–633.
Minimal permutation sets for decoding the binary Golay codes. IEEE Transactions on Information Theory 28 (1982), 541–543. (There is a typo in Table I: the third permutation should have a 6 between the 21 and the 5.)
Computational Number Theory
Factoring polynomials over p-adic fields, with David Cantor. In Algorithmic Number Theory (ANTS IV), LNCS 1838 (2000), 185–208.
A survey of fast exponentiation algorithms. Journal of Algorithms 27 (1998), 129–146.
Discrete logarithms in GF(p) using the number field sieve. SIAM Journal on Discrete Mathematics 6 (1993), 124–138.
Massively parallel computation of discrete logarithms, with K. S. McCurley. In Advances in Cryptology—CRYPTO ‘92, 312–323.
Designing and detecting trapdoors for discrete log cryptosystems. In Advances in Cryptology—CRYPTO ‘92, 66–75.
Fast exponentiation with precomputation, with E. F. Brickell, K. S. McCurley, and D. B. Wilson. In Advances in Cryptology—EUROCRYPT ‘92, 200–207.
The distribution of Lucas and elliptic pseudoprimes, with Carl Pomerance. Mathematics of Computation 57 (1991), 825–838.
On the number of elliptic pseudoprimes. Mathematics of Computation 52 (1989), 231–245.
Pseudoprimes on elliptic curves. In Proceedings of the 1987 Laval University International Number Theory Conference, 290–305.
Miscellaneous
On the density of the set of known Hadamard orders, with Warwick de Launey. Cryptography and Communications 2 (2010), 233–246. arXiv
A comment on the Hadamard conjecture, with Warwick de Launey. Journal of Combinatorial Theory, Series A 95 (2001), 180–184.
Dense admissible sets, with Gene Rodemich. In Algorithmic Number Theory (ANTS III), LNCS 1423 (1998), 216–225.
On sequences without geometric progressions, with Brienne E. Brown. Mathematics of Computation 65 (1996), 1749–1754.
Minimum degree games for graphs, with Frank Harary and Robert Robinson. Discrete Mathematics 128 (1994), 151–163.
Computing the Mordell–Weil rank of curves of genus 2, with David Grant. Transactions of the American Mathematical Society 337 (1993), 807–824.
Percolation in high dimensions. Journal of the London Mathematical Society 44 (1991), 373–384.
Parallel sorting on Cayley graphs. Algorithmica 6 (1991), 554–564.
Hecke operators and the fundamental domain for SL(3,Z), with D. Grenier and A. Terras. Mathematics of Computation 48 (1987), 159–178.