Kuijper, Margreta (Univ. of Melbourne), Pinto, Raquel (Univ. of Aveiro), Polderman, Jan Willem (Univ. of Twente)

Kernel Representations for Behaviors Over Finite Rings

Scheduled for presentation during the Mini-Symposium "Behavioral systems theory" (FrA11), Friday, July 28, 2006, 10:50−11:15, Room 104a

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

Finite rings are important in various communications disciplines. For example, in error-correction coding the importance of codes over finite rings, such as Z_{p^r} has been re-inforced since the early nineties when a breakthrough connection was made between nonlinear binary codes and linear codes over Z_4. Another application consists of modulation codes which employ the algebraic structure of Z_{p^r}.

With these applications in mind some fundamental questions on behaviors over Z_{p^r} are considered. More specifically the paper focuses on so-called kernel representations, i.e. sets of difference equations. The fundamental question how two kernel representations that represent the same behavior are algebraically related turns out to be much less straightforward than in the field case.