Time-domain description of behaviors over finite fields

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    Abstract

    We consider autonomous behaviors over a finite field with characteristic values that do not necessarily belong to the field. The time domain description of the behavior is given in a suitable field extension of the base field. The problem that we consider is how to derive a description completely within the base field. For the case of behaviors over the reals there is a common splitting field for all irreducible polynomials, the complex field. Complex trajectories induce real trajectories by restricting coefficients of complex conjugate exponentials to be complex conjugate as well. For the case of finite fields the situation is more complicated as there does not exist a single finite field extension in which all polynomials over the base field split. In this paper we describe a systematic procedure to obtain explicit expressions for all trajectories in the behavior whose components take values in the base field.
    Original languageEnglish
    Pages (from-to)1258-1266
    Number of pages9
    JournalLinear algebra and its applications
    Volume436
    Issue number5
    DOIs
    Publication statusPublished - 2012

    Keywords

    • MSC-93A10
    • MSC-39A06
    • MSC-12E20
    • Finite field
    • Behavior

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