Polylinear Recurring Sequences over a Bimodule

V. L. Kurakin, A. V. Mikhalev and A. A. Nechaev ()
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V. L. Kurakin: Moscow State University, Center of New Informational Technologies
A. V. Mikhalev: Moscow State University, Center of New Informational Technologies
A. A. Nechaev: Moscow State University, Center of New Informational Technologies

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 484-495 from Springer

Abstract: Abstract The main goal of the paper is to extend some of the known results of the theory of polylinear recurring sequences over fields and their generalizations for sequences over modules with commutative rings of coefficients to the case of noncommutative rings of coefficients. Possible noncommutativity of the main ring causes to consider polylinear sequences over a bimodule. To estimate linear complexity of the sequences in question we consider the notion of polylinear (k-linear) shift register. In fact, the theory of polylinear recurring sequences over fields admits a rather complete extension in this generality if the main bimodule is an Artinian duality context.

Keywords: Commutative Ring; Left Ideal; Shift Register; Endomorphism Ring; Monic Polynomial (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-3-662-04166-6_46

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