Publications

Papers organized by subject:

• Covering Designs
• Difference Sets
• Coding Theory
• Computational Number Theory
• Miscellaneous

• 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 A, 75 (1996), pp. 270-280.
• New constructions for covering designs, (with Greg Kuperberg and Oren Patashnik), Journal of Combinatorial Designs, 3 (1995), pp. 269-284.
• C(12,6,3)=15, (with Oren Patashnik, John Petro and Herb Taylor), Ars Combinatorica, 40 (1995), pp. 161-177.

Difference Sets and Related Designs

• Signed Difference Sets, Designs, Codes and Cryptography, 91 (2023), pp. 2107-2115.
• New Nonexistence Results on Circulant Weighing Matrices, (with K.T. Arasu and Yiran Zhang) , Cryptography and Communications, 13 (2021), pp. 775–789.
• On Difference sets with small lambda, J. Algebraic Combinatorics, 55 (2022), pp. 109–115.
• A Survey of the Multiplier Conjecture, (with Bernhard Schmidt) , Designs, Codes and Cryptography, 78 (2016), pp. 221-236.
• On the existence of cyclic difference sets with small parameters, (with Len Baumert), Proceedings of Conference in Number Theory in Honour of Professor H.C. Williams, 2003.
• Some restrictions on orders of abelian planar difference sets, Journal of Combinatorial Mathematics and Combinatorial Computing, 29 (1999), pp. 241-246.
• The Prime Power Conjecture is true for n < 2,000,000, Electronic Journal of Mathematics, 1 (1994), Paper R6.

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), pp.984-991.

• Perfect single error-correcting codes in the Johnson scheme, IEEE Transactions on Information Theory, 52 (2006), pp. 4670–4672.

• A remark on Plotkin’s bound, (with Warwick de Launey), IEEE Transactions on Information Theory, 47 (2001), pp. 352-355.
• Equidistant arithmetic codes and character sums, Journal of Number Theory, 46 (1994), pp. 323-333.
• Perfect multiple error-correcting arithmetic codes, Mathematics of Computation, 49 (1987), pp. 621-633.
• Minimal permutation sets for decoding the binary Golay codes, IEEE Transactions on Information Theory, 28 (1982), pp. 541-543.

NOTE: There is a typo in Table I, which was found by Cary Huffman. 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 Proceedings of ANTS IV, LNCS 1838 (2000), pp. 185-208.

• A survey of fast exponentiation algorithms, Journal of Algorithms, 27 (1998), pp. 129-146.
• Discrete logarithms in GF(p) using the number field sieve, SIAM J. Discrete Math., 6 (1993), pp. 124-138.
• Massively parallel computation of discrete logarithms, (with K.S. McCurley), Advances in Cryptology- Crypto ’92, pp. 312-323.
• Designing and detecting trapdoors for discrete log cryptosystems, Advances in Cryptology- Crypto ’92, pp. 66-75.
• Fast exponentiation with precomputation (with E.F. Brickell, K.S. McCurley and D.B. Wilson), in Proceedings of Eurocrypt ’92, pp. 200-207.
• The distribution of Lucas and elliptic pseudoprimes, (with Carl Pomerance), Mathematics of Computation, 57 (1991) pp. 825-838.
• On the number of elliptic pseudoprimes, Mathematics of Computation, 52 (1989), pp. 231-245.
• Pseudoprimes on elliptic curves, Proceedings of the 1987 Laval University International Number Theory Conference, pp. 290-305.

Miscellaneous

• • Math Databases on the Cheap, lightning talk at LuCaNT, July 2023.
  • How to proceed in mathematics, (with Skip Garibaldi), AMS Notices, 68 (2021), pp. 748-749.
  • On the density of the set of known Hadamard orders, (with Warwick de Launey), Cryptography and Communications, 2 (2010), pp. 233-246.
  • A Comment on the Hadamard Conjecture, (with Warwick de Launey), J. Combinatorial Theory A, 95 (2001), pp. 180-184.
  • Dense admissible sets, (with Gene Rodemich), Proceedings of ANTS III, LNCS 1423 (1998), pp. 216-225.
  • On sequences without geometric progressions, (with Brienne E. Brown), Mathematics of Computation, 65 (1996), pp. 1749-1754.
  • Degree games for graphs, (with Frank Harary and Robert Robinson), Discrete Mathematics, 128 (1994), pp. 151-163.
  • Computing the Mordell-Weil rank of curves of genus 2, (with David Grant), Transactions of the American Math. Soc., 337 (1993), pp. 807-824.
  • Percolation in high dimensions, Journal of the London Math. Soc., (2) 44 (1991), pp. 373-384.
  • Parallel sorting on Cayley graphs, Algorithmica, 6 (1991), pp. 554-564.
  • Hecke operators and the fundamental domain for SL(3,Z), (with D. Grenier and A. Terras), Mathematics of Computation, 48 (1987), pp. 159-178.