VIJAY K. BHARGAVA President, IEEE Information Theory Society Department of Electrical and Computer Engineering University of Victoria, Victoria

Title: POWER-RESIDUES, BINARY MATRICES WITH SPECIFIED PROPERTIES AND ERROR CORRECTING CODES

Monday, October 23, 2000 at 11:30 a.m. in Room ASB 9898

The binary matrices A which are circulant with one or more of the following properties: (1) A is symmetric, i.e., A = A^{T}, (2) A is orthogonal, i.e. AA^{T} = I (mod 2), (3) A has low multiplicative order, i.e., A^{m} = I, occur often in communication, control and network theory problems. In this talk we construct a number of such matrices. The results are based on the theory of power-residues modulo an odd prime p, and the fact that the algebra of all p x p circulant matrices is isomorphic to the algebra of polynomials modulo (x^{p} - 1). For p a prime of the form 8m + 3 or 8m - 3, the resulting matrices can be used to construct (2p + 2, p + 1) codes of Karlin and McWilliams which are the binary images of (p + 1, (p + 1)/2) extended quadratic residues codes over GF(4). For higher power-residues, the resulting binary matrices are rather sparse and can be used to construct some interesting error correcting codes.

Biography

Vijay K. Bhargava received the B. Sc., M. Sc., and Ph. D. degrees from Queen's University, Kingston, Canada in 1970, 1972 and 1974 respectively.

Currently, he is Professor of Electrical and Computer Engineering at the University of Victoria. He is a co-author of the book DIGITAL COMMUNICATIONS BY SATELLITE (New York: Wiley, 1981) and co-editor of the IEEE press book REED-SOLOMON CODES AND THEIR APPLICATIONS. He is an Editor-in-Chief of WIRELESS PERSONAL COMMUNICATION, a Kluwer Periodical. His research interests are in multi-media wireless communications.

Dr. Bhargava is very active in the IEEE and is currently the President of the IEEE Information Theory Society. He was Co-chair for IEEE ISIT'95, Technical Program Chair for IEEE ICC'99 and is the Chair of IEEE VTC'2002 Fall, to be held in Vancouver.

Dr. Bhargava is a Fellow of the B.C. Advanced Systems Institute, Engineering Institute of Canada (EIC), the IEEE and the Royal Society of Canada. He is a recipient of the IEEE Centennial Medal (1984), IEEE Canada's McNaughton Gold Medal (1995), the IEEE Haraden Pratt Award (1999) and the IEEE Third Millennium Medal (2000).

^{*} Currently on sabbatical leave at the Hong Kong University of Science and Technology.

Last updated Monday September 18 20:41:00 PDT 2000.