Solomon W. Golomb
University of Southern California
Election Year: 2003
Primary Section: 34, Computer and Information Sciences
Secondary Section: 11, Mathematics
Membership Type: Member
Much of my technical work has consisted of applying areas of previously "inapplicable" discrete mathematics, including number theory, finite algebraic structures, and combinatorial designs, to problems involving coding or signal design for a wide variety of communications situations. Starting with the analysis of maximum-length linear shift register sequences (m-sequences) via polynomials over finite fields, I have studied the existence and properties of other periodic binary sequences having the same auto-correlation behavior as m-sequences. These are particularly useful for radar and sonar, and in CDMA cellular systems. My research involving nonlinear shift register sequences concerns their applicability and limitations in cryptographic systems, and their use in radar and ranging over interplanetary distances. I have also investigated the best classes of signals for a wide variety of radar applications, suggested new source coding methods for geometrically distributed source messages, considered optimum error correcting codes relative to a variety of "error metrics", such as the Lee metric, and studied comma-free codes for message synchronization. In recreational mathematics I am best known as the inventor of "polyominoes", and in analytic number theory, for a new method of estimating the densities of certain patterns of primes.