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Two-dimensional shift register synthesis and Gröbner bases for polynomial ideals over an integer residue ring

Authors
Journal
Discrete Applied Mathematics
0166-218X
Publisher
Elsevier
Publication Date
Volume
33
Identifiers
DOI: 10.1016/0166-218x(91)90115-d
Disciplines
  • Computer Science

Abstract

Abstract In this paper we present an algorithm for finding a simplest n-dimensional linear feedback shift register which generates a given n-dimensional array over the integer residue ring Z m , where the term simplest means that the degree of every connection polynomial is minimal. This problem is an extension of the (one-dimensional) shift register synthesis over a field not only to n dimensions but also over the ring Z m . The result is useful for implementing encoders and decoders of Abelian codes over Z m .

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