Journal of Mathematical Sciences

, Volume 80, Issue 5, pp 2161–2173 | Cite as

On Poincaré series for codes

  • V. E. Govorov


The paper deals with an alphabet-code model and with an associative algebra over a field generated by the alphabet for which the code words are the determinant relations. The restrictions on the overlapping of the code words are closely connected to the restrictions on the homology groups of the algebra. The paper presents the study of this connection quantitatively expressed via the Poincaré series of the algebra. Bibliography: 6 titles.


Homology Group Associative Algebra Code Word Determinant Relation 
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Literature Cited

  1. 1.
    H. Cartan and S. Eilenberg,Homological Algebra, Princeton Univ. Press (1956).Google Scholar
  2. 2.
    I. Herstein,Noncommutative rings, New York (1968).Google Scholar
  3. 3.
    A. A. Markov,Introduction to code theory [in Russian], Nauka, Moscow (1982).Google Scholar
  4. 4.
    V. E. Govorov, “Dimension and multiplicity of graded algebras,”Sib. Mat. Zh.,14, No. 6, 1200–1206 (1973).MATHMathSciNetGoogle Scholar
  5. 5.
    V. E. Govorov, “Graded algebras,”Mat. Zametki,12, No. 2, 197–204 (1972).MATHMathSciNetGoogle Scholar
  6. 6.
    V. V. Levenstein, “On some properties of coding in self-adaptive automata for decoding messages,”Probl. Kibern.,11, 88–90 (1964).MathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. E. Govorov

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