Talk abstract:

Linear Systems over Fields and Rings, Linear Complexity, and Fourier Transforms

James L. Massey
ETH Zurich and Lund University

This mostly tutorial presentation will review the definition of the linear complexity of a sequence over a field or a commutative ring, give an elementary proof that the linear complexity is the smallest dimension of a single-output linear system that can produce the sequence as its zero-input response, present a simple necessary and sufficient condition for the existence of a generalized discrete Fourier Transform of a prescribed length N, and show the connection between the linear complexity of a periodic sequence and the generalized Discrete Fourier Transform of its first period.

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