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An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2227))

Abstract

An algorithm for calculating a set ofgenerators ofrepresentative 2-cocycles on semidirect product offinite abelian groups is constructed, in light ofthe theory over cocyclic matrices developed by Horadam and de Launey in [7],[8]. The method involves some homological perturbation techniques [3],[1], in the homological correspondent to the work which Grabmeier and Lambe described in [12] from the viewpoint ofcohomology . Examples ofexplicit computations over all dihedral groups D 4t are given, with aid of Mathematica.

All authors are partially supported by the PAICYT research project FQM-296 from Junta de Andalucía and the DGESIC research project PB98-1621-C02-02 from Education and Science Ministry (Spain).

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References

  1. V. Álvarez, J.A. Armario, M.D. Frau and P. Real. Homology ofsemidirect products offinite abelian groups with group action. Preprint of Dpto. Matemática Aplicada I, University ofSeville (Spain, 2001).

    Google Scholar 

  2. V. Álvarez, J.A. Armario, M.D. Frau and P. Real. Homology ofsemidirect products ofgroups: algorithms and applications. Preprint of Dpto. Matemática Aplicada I, University ofSeville (Spain, 2001).

    Google Scholar 

  3. V. Álvarez, J.A. Armario, P. Real. On the homology o fsemi-direct products ofgroups. Colloquium on Topology, Gyula (Hungary, 1998).

    Google Scholar 

  4. J.A. Armario, P. Real and B. Silva. On p-minimal homological models oft wisted tensor products ofelemen tary complexes localized over a prime. Contemporary Mathematics, 227, 303–314, (1999).

    MathSciNet  Google Scholar 

  5. K.S. Brown. Cohomology ofgroups. Graduate Texts in Math., 87, Springer-Verlag, New York (1982).

    Google Scholar 

  6. W. de Launey and K.J. Horadam. A weak difference set construction for higherdimensional designs. Designs, Codes and Cryptography, 3, 75–87, (1993).

    Article  MATH  Google Scholar 

  7. W. de Launey and K.J. Horadam. Cocyclic development ofdesigns, J. Algebraic Combin., 2 (3), 267–290, 1993. Erratum: J. Algebraic Combin., (1), pp. 129, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  8. W. de Launey and K.J. Horadam. Generation ofco cyclic Hadamard matrices. Computational algebra and number theory (Sydney, 1992), volume 325 of Math. Appl., 279–290. Kluwer Acad. Publ., Dordrecht, (1995).

    Google Scholar 

  9. D.L. Flannery. Transgression and the calculation ofco cyclic matrices. Australas. J. Combin., 11, 67–78, (1995).

    MATH  MathSciNet  Google Scholar 

  10. D.L. Flannery. Calculation ofco cyclic matrices. J. of Pure and Applied Algebra, 112, 181–190, (1996).

    Article  MATH  MathSciNet  Google Scholar 

  11. D.L. Flannery and E.A. O’Brien. Computing 2-cocycles for central extensions and relative difference sets. Comm. Algebra, 28(4), 1939–1955, (2000).

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Grabmeier, L.A. Lambe. Computing Resolutions Over Finite p-Groups. Proceedings ALCOMA’99. Eds. A. Betten, A. Kohnert, R. Lave, A. Wassermann. SpringerLecture Notes in Computational Science and Engineering,Springer-Verlag, Heidelberg, (2000).

    Google Scholar 

  13. V.K.A.M. Gugenheim and L.A. Lambe. Perturbation theory in Differential Homological Algebra, I. Illinois J. Math., 33, 556–582, (1989).

    MathSciNet  Google Scholar 

  14. V.K.A.M. Gugenheim, L.A. Lambe and J.D. Stashe.. Perturbation theory in Differential Homological Algebra II, Illinois J. Math., 35(3), 357–373, (1991).

    MATH  MathSciNet  Google Scholar 

  15. K.J. Horadam and A.A.I. Perera. Codes from cocycles. Lecture Notes in Computer Science, volume 1255, 151–163, Springer-Verlag, Berlin-Heidelberg New York, (1997).

    Google Scholar 

  16. J. Huebschmann. Cohomology ofnilp otent groups ofclass 2. J. Alg., 126, 400–450, (1989).

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Huebschmann. Cohomology ofmetacyclic groups. Transactions of the American Mathematical Society, 328(1), 1–72, (1991).

    Article  MATH  MathSciNet  Google Scholar 

  18. L.A. Lambe and J.D. Stashe.. Applications ofp erturbation theory to iterated fibrations. Manuscripta Math., 58, 367–376, (1987).

    Article  Google Scholar 

  19. S. Mac Lane. Homology. Classics in Mathematics Springer-Verlag, Berlin, (1995). Reprint ofthe 1975 edition.

    Google Scholar 

  20. P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications, 2, 51–88, (2000).

    MATH  MathSciNet  Google Scholar 

  21. K. Tahara. On the Second Cohomology Groups ofSemidirect Products. Math Z., 129, 365–379, (1972).

    Article  MATH  MathSciNet  Google Scholar 

  22. O. Veblen. Analisis situs. A.M.S. Publications, 5, (1931).

    Google Scholar 

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Authors and Affiliations

  1. Dpto. Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012, Sevilla, Spain

    V. Álvarez, J.A. Armario, M.D. Frau & P. Real

Authors
  1. V. Álvarez
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  2. J.A. Armario
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  3. M.D. Frau
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  4. P. Real
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Editor information

Editors and Affiliations

  1. Department of Mathematics, RMIT University, GPO Box 2476V, 3001, Melbourne, Australia

    Serdar Boztaş

  2. Department of Computing, Macquarie University, 2109, NSW, Australia

    Igor E. Shparlinski

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Álvarez, V., Armario, J., Frau, M., Real, P. (2001). An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_30

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  • DOI: https://doi.org/10.1007/3-540-45624-4_30

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  • Print ISBN: 978-3-540-42911-1

  • Online ISBN: 978-3-540-45624-7

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