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Singular shift registers over residue class rings

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Abstract

The study of shift registers over the ringZ p r (p a prime,r ≥ 1), in particular the singular case, is carried out, giving necessary and sufficient conditions to make a shift register singular. Its state graph is characterized as a tree, whose form depends on the characteristic polynomial of the shift register. The relationships with singular shift register overZ p are explored and a proof of their equivalence is presented.

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References

  1. A. Gill,Linear Sequential Circuits: Analysis, Synthesis and Applications, McGraw-Hill Book Co., New York, 1967.

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  2. M. Harrison,Lectures on Linear Sequential Machines, Academic Press, New York, 1969.

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  3. S. Lang,Algebra, Addison-Wesley Publishing Co., Reading, Mass., 1967.

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  4. M. Magidin andA. Gill, “Decomposition of linear sequential circuits over residue class rings,”J. Franklin Inst. 294 (1972), 167–180.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Iztapalapa, México 13, D.F., Mexico

    Mario Magidin

  2. Electronics Research Laboratory Dept. of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA

    Arthur Gill

Authors
  1. Mario Magidin
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  2. Arthur Gill
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Additional information

Research sponsored by the National Science Foundation, Grant GK-1065x, and the Joint Services Electronics Program, Grant AFOSR-68-1488.

Part of this work was done while the author was at Electronics Research Laboratory, University of California at Berkeley.

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Magidin, M., Gill, A. Singular shift registers over residue class rings. Math. Systems Theory 9, 345–358 (1975). https://doi.org/10.1007/BF01715360

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  • DOI: https://doi.org/10.1007/BF01715360

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