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Information Rates and Weights of Codes in Structural Matrix Rings

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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

Several efficient error-correcting codes are ideals in certain ring constructions. We consider two-sided ideals in structural matrix rings defined in terms of directed graphs with the set of vertices corresponding to rows and columns, and with edges corresponding to nonzero entries in matrices of the ring. Formulas for Hamming weights of all ideals in structural matrix rings are found and sharp upper bounds for information rates of these ideals are given.

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Author information

Authors and Affiliations

  1. Faculty of Science and Engineering, University of Tasmania, Hobart, Box 252-37, 7001, Tasmania, Australia

    Andrei Kelarev

  2. Institute of Computer Science, Tartu University, J. Liivi 2, 50409, Tartu, Estonia

    Olga Sokratova

Authors
  1. Andrei Kelarev
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  2. Olga Sokratova
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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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© 2001 Springer-Verlag Berlin Heidelberg

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Kelarev, A., Sokratova, O. (2001). Information Rates and Weights of Codes in Structural Matrix Rings. 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_16

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  • DOI: https://doi.org/10.1007/3-540-45624-4_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42911-1

  • Online ISBN: 978-3-540-45624-7

  • eBook Packages: Springer Book Archive

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