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Construction and Categories of Codes

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Information Security and Privacy (ACISP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1841))

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Abstract

Blakley and Borosh introduced a general theory of codes, encompassing cryptographic and error control codes among others. They explored the properties of such general codes with methods from relational algebra and set theory. We provide a categorical point of view, which leads to new constructions of codes. We also exhibit a Jordan-Hölder type theorem and a Schreier refinement technique.

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References

  1. Arbib, M.A., Manes, E.: Arrows, Structures, and Functors – The Categorical Imperative. Academic Press, New York (1975)

    MATH  Google Scholar 

  2. Blakley, G.R., Borosh, I.: A general theory of codes, I: Basic concepts. In: Dorninger, D., Eigenthaler, G., Kaiser, H.K., Kautschistsch, H., More, W. (eds.) Proceedings of the Klagenfurt Conference, Contributions to General Algebra, vol. 10, pp. 1–29. Verlag Johannes Heyn, Klagenfurt, Austria (1998)

    Google Scholar 

  3. Blakley, G.R., Borosh, I.: A general theory of codes, II: Paradigms and homomorphisms. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 1–30. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Calderbank, A.R., Sloane, N.J.A.: Modular and padic cyclic codes. Designs, Codes, and Cryptography 6, 21–35 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cohn, P.M.: Universal Algebra. D. Reidel Publishing Company, Dordrecht (1981) (revised edition)

    MATH  Google Scholar 

  6. Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inform. Theory 22, 644–654 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mac Lane, S.: Categories for the Working Mathematician. Springer, Berlin (1971)

    MATH  Google Scholar 

  8. Pohlig, S.C., Hellman, M.E.: An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Trans. Inform. Theory 24, 106–110 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  9. Purdy, G.P.: A high-security log-in procedure. Comm. of the ACM 17(4), 442–445 (1974)

    Article  MathSciNet  Google Scholar 

  10. Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Comm. ACM 21, 120–126 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA.

    G. R. Blakley, I. Borosh & A. Klappenecker

Authors
  1. G. R. Blakley
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  2. I. Borosh
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  3. A. Klappenecker
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Editor information

Editors and Affiliations

  1. Information Security Research Centre, Queensland University of Technology, GPO Box 2434, 4000, Brisbane, Queensland, Australia

    E. P. Dawson , A. Clark  & Colin Boyd ,  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Blakley, G.R., Borosh, I., Klappenecker, A. (2000). Construction and Categories of Codes. In: Dawson, E.P., Clark, A., Boyd, C. (eds) Information Security and Privacy. ACISP 2000. Lecture Notes in Computer Science, vol 1841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10718964_22

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  • DOI: https://doi.org/10.1007/10718964_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67742-0

  • Online ISBN: 978-3-540-45030-6

  • eBook Packages: Springer Book Archive

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