Papers on
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 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
On Cyclic Difference Sets,
(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)
submitted to IEEE Transactions on Information Theory.
Here are
slides
from a talk at the 2009 Information Theory and Applications workshop
at UCSD.
Perfect single error-correcting codes in the Johnson scheme,
IEEE Transactions on Information Theory, 52 (2006), pp. 4670--4672.
Here are
slides
from a talk at the 2007 Information Theory and Applications workshop
at UCSD.
A remark on Plotkin's bound,
(with Warwick Delauney)
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,
Factoring polynomials over p-adic fields,
(with David Cantor)
A survey of fast exponentiation algorithms,
Discrete logarithms in GF(p) using the number field sieve
Massively parallel computation of
discrete logarithms,
(with K.S. McCurley)
Designing and detecting trapdoors for discrete log
cryptosystems,
Fast exponentiation with precomputation
(with E.F. Brickell, K.S. McCurley and D.B. Wilson)
The distribution of Lucas and elliptic
pseudoprimes,
(with Carl Pomerance)
On the number of elliptic pseudoprimes,
Pseudoprimes on elliptic curves,
A Comment on the Hadamard Conjecture,
(with Warwick Delauney)
Dense admissible sets,
(with Gene Rodemich)
On sequences without geometric
progressions,
(with Brienne E. Brown)
Degree games for
graphs,
(with Frank Harary and Robert Robinson)
Computing the Mordell-Weil rank of curves
of genus 2,
(with David Grant)
Percolation in high dimensions,
Parallel sorting on Cayley graphs,
Hecke operators and the
fundamental domain for SL(3,Z),
(with D. Grenier and A. Terras)
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
Proceedings of ANTS IV, LNCS 1838 (2000), pp. 185-208.
Here are
slides
from the ANTS talk.
Journal of Algorithms, 27 (1998), pp. 129-146.
SIAM J. Discrete Math., 6 (1993), pp. 124-138.
Advances in Cryptology- Crypto '92, pp. 312-323.
Advances in Cryptology- Crypto '92,
pp. 66-75.
Proceedings of Eurocrypt 92, pp. 200-207.
Mathematics of Computation, 57 (1991) pp. 825-838.
Mathematics of Computation,
52 (1989), pp. 231-245.
Proceedings of the 1987 Laval University
International Number
Theory Conference,
pp. 290-305.
Miscellaneous
JCT A, 95 (2001), pp. 180-184.
Proceedings of ANTS III, LNCS 1423 (1998), pp. 216-225.
Mathematics of Computation, 65 (1996),
pp. 1749-1754.
Discrete Mathematics, 128 (1994), pp. 151-163.
Transactions of the American Math. Soc.,
337 (1993), pp. 807-824.
Journal of the London Math. Soc.,
(2) 44 (1991), pp. 373-384.
Algorithmica,
6 (1991), pp. 554-564.
Mathematics of Computation,
48 (1987), pp. 159-178.