Dr. James Davis
Professor of Mathematics
Profile

Dr. Davis is interested in questions that require algebraic techniques to solve combinatorial problems. He has done work in difference sets and related objects, bent functions, and error correcting codes with an emphasis on finding new constructions with optimal or near-optimal structure. He has also worked in an industrial research lab (Hewlett-Packard) and served as a testifying expert in a patent dispute between Apple and Samsung.

He has 15 granted patents including:
K.K. Smith, J. Jedwab, J.A. Davis, D. Banks and S.R. Wyatt, System for error correction coding and decoding, U.S. Patent No. 7418644, 26 Aug 2008.
D. Banks, J. Davis, and J. Jedwab, Identifying uncorrectable codewords in a Reed-Solomon decoder for errors and erasures, US Patent No. 7278086, 2 October 2007.
J. Davis, K. Eldredge, J. Jedwab, G. Seroussi, and K. Smith, MRAM with controller, US Patent No. 7266732, 4 September 2007.

Grants and Fellowships

National Security Agency Grant, 2015

National Science Foundation, LURE, 2007-2011, $1,500,000.

National Security Agency Grant, salary, travel expenses, and support for undergraduate research, January 2003-December 2005.

University of Richmond Undergraduate Research Commmittee Collaborative Grant, salary and travel for me and two students, summer 2002.

Hewlett-Packard Grant for Leave of Absence, academic year 2000-2001, paying salary, moving expenses, cost of living expenses, and benefits.

Awards
University of Richmond Outstanding Mentor Award, 2004.
Presentations
Linking systems in non elementary abelian groups, Combinatorics 2014 conference, Gaeta, Italy, June 9, 2014.

Apple-Samsung: the codes in 3G communication, Finite Fields conference, Magdeburg, Germany, July 25, 2013.

Apple-Samsung: a personal story, University of Richmond, August 2012.
Institutional Service
Presidential Search Committee, 2014-present

Science Scholar Committee, 1994-present
Publications
Articles
Linking systems in nonelementary abelian groups, with J. Polhill and W. Martin, J. Comb. Th. (A), Vol. 123 Issue 1, 92-103, April 2014.
A comparison of Carlet's nonlinearity bounds, with G. McGrew, D. Steele, and K. Marsden, submitted.
New product constructions of partial difference sets, with J. Polhill and K. Smith, Designs, Codes, and Cryptography, Online First, 11 February 2012.
Novel Classes of Minimal Delay and Low PAPR Rate 1/2 Complex Orthogonal Designs, with S. Adams, N. Karst, M. K. Murugan, B. Lee, IEEE Trans. on Inf. Th., Vol. 57 issue 4, 2254-2262, April 2011.
Davis, J., & Poinsot, L. (2008) G-perfect Nonlinear Functions. Designs, Codes and Cryptography, 46:1 January.
Davis J., Crouch, S., & Jedwab, J. (2007) The design of the IEEE 802.12 coding scheme. IEEE Transactions on Communications, October.
Davis, J., Jedwab, J., & Smith, K. (2007) Proof of the Barker array conjecture. Proceedings of the AMS, Vol. 135, 2011-2018.
Davis, J., & Xiang, Q. (2006) New amorphic association schemes. Finite Fields and their Applications, Vol. 12, 595-612.
Davis, J., & Xiang, Q. (2004) Negative Latin square type partial difference sets in nonelementary abelian 2-groups. Journal of London Mathematical Society, Vol. 70 issue 1, 125-141.
Davis, J., & Smeltzer, D. (2003) Exponential numbers of inequivalent difference sets in Z_{2^{s+1}}^2. Journal of Combinatorial Designs, Vol. 11 number 4, 249-259.

Davis, J., & Xiang, Q. (2000) A Family of partial difference sets with Denniston parameters in nonelementary abelian 2-groups. The European Journal of Combinatorics, Vol. 00, 1-8.

Davis, J., & Xiang, Q. (2000) Constructions of low rank relative difference sets in 2-groups using Galois rings. Finite Fields and their Applications 6, 130-145.
Davis, J., & Jedwab, J. "A unified approach to difference sets with gcd(v,n)>1," in T.Helleseth et al.,eds., NATOScience Series C, Difference Sets, Sequences and Their Correlation Properties, Vol. 542, Kluwer Academic Publishers, editor A. Pott and others, 85-112, Dordrecht.
Davis, J., Jedwab, J., & Paterson, K. "Codes, correlations and power control in OFDM," in T.Helleseth et al., eds., NATO Science Series C, Difference Sets, Sequences and Their Correlation Properties, Vol. 542, Kluwer Academic Publishers, editor A. Pott and others, 113-132, Dordrecht.
Davis, J., & Jedwab, J. (1999) A new family of relative difference sets in 2-groups. Designs, Codes, and Cryptography Memorial Volume for Ed Assmus, Vol. 17, 305-312.
Davis, J., & Jedwab, J. (1999) 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.
A unifying construction for difference sets, with J.Jedwab, Journal of Combinatorial Theory Series (A), 
Vol. 80 No.1, 13-78, Oct. 1997.
Chapters

Davis, J.,  & Jedwab, J. (1999) "Some recent developments in difference sets," in K. Quinn, B. Webb, F. Holroyd and C. Rowley, eds., Pitman Research Notes in Mathematics,Combinatorial Designs and their Applications, Addison Wesley Longman, 83-102.

Additional Publications
Shared Autocorrelation property of sequences, with C. Bodea, C. Copos, M. Der, and D. O'Neal, IEEE Transactions on Information Theory, Vol. 57 issue 6, 3805-3809, June 2011.

Education
Ph.D., University of Virginia 1987
Mathematics
M.S., University of Virginia 1985
Mathematics
B.S., Lafayette College 1983
Mathematics
Contact Information
(804) 289-8094
Areas of Expertise
Algebra
Combinatorics
Number Theory
Coding Theory