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International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 2001: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 57–66Cite as

Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance

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

Abstract

We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and [32, 16, 12] by using the [8, 4, 6] octacode. Moreover, there is a natural Tanner graph associated to the construction of [3], and it turns out that all our constructions have Tanner graphs that have a cyclic structure which gives tail-biting trellises of low complexity: 16-state tail-biting trellises for the [24, 12, 8], [32, 16, 8], [40, 20, 8] binary codes, and 256-state tail-biting trellises for the [24, 12, 12] and [32, 16, 12] codes over Z4.

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Author information

Authors and Affiliations

  1. France Telecom R&D, DMR/DDH, CCETT-Rennes, 35512, Cesson-Sévigné, France

    E. Cadic & J.C. Carlach

  2. LRI, Université Paris-Sud, 91405, Orsay, France

    G. Olocco & J.P. Tillich

  3. University of Limoges/LACO, 123 avenue Albert Thomas, 87060, Limoges, France

    A. Otmani

Authors
  1. E. Cadic
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  2. J.C. Carlach
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  3. G. Olocco
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  4. A. Otmani
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  5. J.P. Tillich
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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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Cadic, E., Carlach, J., Olocco, G., Otmani, A., Tillich, J. (2001). Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance. 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_6

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  • DOI: https://doi.org/10.1007/3-540-45624-4_6

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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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