The paper under
review clearly ranks as one of the most important papers in the general
area of difference sets
ever written. I will just mention the most striking results that make it important: It contains the first new
parameter family of difference sets found since 1977. It gives a unifying theory which allows one to produce a
difference set with $(\nu,n)>1$ in every abelian group which is known to contain such a difference set.....
It characterises a certain class of groups containing McFarland difference sets..... In particular, the celebrated
characterization theorem for those abelian 2-groups which contain a difference set (a problem which took decades
to settle) becomes a trivial corollary....
Reviewer: Jungnickel, Dieter (D-AGSB)
Peak-to-mean power control in OFDM,
Golay complementary sequences and Reed-Muller codes, with
J.Jedwab, IEEE Transactions on Information Theory, Vol. 45, 2397-2417, 1999.
OFDM is a proposed transmission scheme designed to provide more reliable and quicker communication
between mobile devices. This paper demonstrates that the use of Golay complementary sequences
simultaneously controls the required transmission power and provides efficient error correcting capabilities
through the use of Reed-Muller codes. Also addressed in the paper are flexible implementation possibilities
obtained by trading off code rate, power control, and error correction capability. The problems considered in
this paper arose during my sabbatical year 1995-96 at Hewlett-Packard Laboratories, and it illustrates the
usefulness of theoretical mathematics in answering applied problems in communication engineering.
A Family of partial difference sets
with Denniston parameters in nonelementary abelian 2-groups, with
Q.Xiang, The European Journal of Combinatorics, Vol. 00, 1-8, 2000.
Galois Rings have been powerful tools over the past few years in constructing designs and codes with good
properties. This paper demonstrates that Galois Rings can be used to construct Denniston partial difference
sets in different groups than the original Denniston construction. The project being proposed for the summer
of 2002 is a natural extension of the work found in this paper.
RECENT PRESENTATIONS OF NOTE:
Denniston Partial Difference Sets, The National University of Singapore, June, 2000.
A Unifying Construction for Difference
Sets, parts 1 and 2, NATO conference on difference sets,
sequences, and their correlation properties, Bad Windsheim, Germany, August 4 & 5, 1998
From the Kirkman schoolgirl problem to error correcting codes: different views of difference sets, The
University of Wales at Aberystwyth colloquium, May, 1996.
RECENT UNDERGRADUATE HONORS THESES:
Difference sets, symmetric designs, and coding theory: a look at the incidence matrices for several difference sets,
Kate Nieswand, 2000.
On some new constructions of difference sets, Sarah Spence, 1997.
Generalizations of the mod4 construction of the Nordstrom-Robinson Code, Tim Frey, 1995.
SELECTED SUMMER RESEARCH PROJECTS:
Difference sets in 2-groups and their associated codes,Mohammed Abouzaid and Jamie Bigelow, Summer, 2000.
Sponsored by Hewlett-Packard.
Using the Quantum Computer to break
and Elliptic Curve Cryptosystem, Jodie Eicher and Yaw Opoku,
summer, 1997. This won the Student Research Symposium Natural Science Award at the University of Richmond
in spring, 1998. Sponsored by Hewlett-Packard.
Coding theory over Galois Rings,
Sarah Spence and Brian McKeever, Summer, 1995. This won a poster
presentation at the annual Joint Math meetings of the American Mathematical Society and the Mathematics
Association of America in January, 1996.
Ph.D. Mathematics, University of Virginia, August, 1987. Dissertation: "Difference sets in abelian 2-groups";
Advisor: Dr. Harold Ward.
B.S. Mathematics with Honors, Magna cum laude, Lafayette College, May, 1983.
Chair of Mathematics and Computer Science Department, University of Richmond, 1997-2000.
Professor, University of Richmond, 2001-Present.
Associate Professor, University of Richmond, 1994-2001.
Assistant Professor, University of Richmond, 1988-1994.
Hewlett-Packard Grant for Leave of Absence, academic year 2000-2001, paying salary, moving expenses, cost
of living expenses, and benefits for a year in Bristol, England.
Hewlett-Packard Grant for undergraduate
summer research institute, May 1997-August 2000, to fund 4 students
full time working on applied problems.
Hewlett-Packard sabbatical Grant, August
1995-August 1996, funded move to England, half salary, other
expenses for the academic year.
National Security Agency Young Investigator
Grant, June 1995-June 1997, summer salary and travel.