Dan Gordon's Home Page

This page is a repository for my mathematical publications.  For my online combinatorial databases, see:


Papers organized by subject:

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

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.
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 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)
Proceedings of ANTS IV, LNCS 1838 (2000), pp. 185-208.
Here are
slides from the ANTS talk.

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)
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.


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)
JCT 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.