Perfect single error-correcting codes in the Johnson scheme,
Submitted to IEEE Transactions on Information Theory
(with Douglas Stinson)
Coverings,
Handbook of Combinatorial Designs, second edition,
to appear.
(with Len Baumert)
On Cyclic Difference Sets,
Proceedings of
Conference in Number Theory in Honour of Professor H.C. Williams,
2003, to appear.
(with Warwick Delauney)
A remark on Plotkin's bound,
IEEE Transactions on Information Theory, 47 (2001), pp. 352-355.
(with Warwick Delauney)
A Comment on the Hadamard Conjecture,
JCT A, 95 (2001), pp. 180-184.
(with David Cantor)
Factoring polynomials over p-adic fields,
Proceedings of ANTS IV, LNCS 1838 (2000), pp. 185-208.
Here are
slides
from the ANTS talk. Also, you can see the
GP code implementing our algorithm. It's written for
a proof of concept, and not efficiency.
Some restrictions on orders of abelian planar difference sets,
Journal of Combinatorial Mathematics and Combinatorial
Computing, 29 (1999), pp. 241-246.
(with Gene Rodemich)
Dense admissible sets,
Proceedings of ANTS III, LNCS 1423 (1998), pp. 216-225.
A survey of fast exponentiation algorithms,
Journal of Algorithms, 27 (1998), pp. 129-146.
(with Brienne E. Brown)
On sequences without geometric
progressions,
Mathematics of Computation, 65 (1996),
pp. 1749-1754.
(with Greg Kuperberg, Oren Patashnik and Joel Spencer) Asymptotically optimal covering designs, Journal of Combinatorial Theory A, 75 (1996), pp. 270-280.
(with Greg Kuperberg and Oren Patashnik) New constructions for covering designs, Journal of Combinatorial Designs, 3 (1995), pp. 269-284.
(with Oren Patashnik, John Petro and Herb Taylor) C(12,6,3)=15, Ars Combinatorica, 40 (1995), pp. 161-177.
Equidistant arithmetic codes and character sums, Journal of Number Theory, 46 (1994), pp. 323-333.
The Prime Power Conjecture is true for n < 2,000,000,
Electronic Journal of Mathematics, 1 (1994), Paper R6.
(with Frank Harary and Robert Robinson) Degree games for graphs, Discrete Mathematics, 128 (1994), pp. 151-163.
(with David Grant) Computing the Mordell-Weil rank of curves of genus 2, Transactions of the American Math. Soc., 337 (1993), pp. 807-824.
Discrete logarithms in GF(p) using the number field sieve
SIAM J. Discrete Math., 6 (1993), pp. 124-138.
(with K.S. McCurley) Massively parallel computation of discrete logarithms, Advances in Cryptology- Crypto '92, pp. 312-323.
Designing and detecting trapdoors for discrete log cryptosystems, Advances in Cryptology- Crypto '92, pp. 66-75.
(with E.F. Brickell, K.S. McCurley and D.B. Wilson) Fast exponentiation with precomputation Proceedings of Eurocrypt 92, pp. 200-207.
(with Carl Pomerance) The distribution of Lucas and elliptic pseudoprimes, Mathematics of Computation, 57 (1991) pp. 825-838.
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.
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.
Perfect multiple error-correcting arithmetic codes, Mathematics of Computation, 49 (1987), pp. 621-633.
(with D. Grenier and A. Terras) Hecke operators and the fundamental domain for SL(3,Z), Mathematics of Computation, 48 (1987), pp. 159-178.
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 permuation should have a
6 between the 21 and the 5.
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