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

AAECC 1991: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 360–367Cite as

Completely transitive codes and distance transitive graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 539))

Abstract

The class of completely transitive linear binary codes was introduced in [8] and it is proved that they are completely regular linear codes.

The completely regular binary propelinear codes, a class of completely regular codes, and the e-latticed (e≥3) distance regular graphs, a class of distance regular graphs, are related in [4] and [5].

In this paper we generalize the completely transitive concept to the propelinear binary codes and we show that the class of completely transitive propelinear binary codes is isomorphic to a class of e-latticed distance regular graphs, the distance transitive graphs.

This work was supported in part by Spanish DGICYT/UAB Grant No. 113118

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References

  1. A.Brouwer, A.M.Cohen, A.Neumaier, Distance Regular Graphs. Springer-Verlag, (1989).

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  2. A. Brouwer, A Note on Completely Regular Codes. Discrete Mathematics 83, (1990) 115–117.

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  3. F.J.Macwilliams, N.J.A.Sloane, The Theory of Error-Correcting Codes, (North-Holland Publishing Company, 1977).

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  4. J. Rifà, L. Huguet, Classification of a Class of Distance-Regular Graphs via Completely Regular Codes. Discrete Applied Mathematics 26 (1990) 289–300.

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  5. J. Rifà, Distance Regular Graphs and Propelinear Codes. Springer-Verlag, LNCS 357, (1989) 341–355.

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  6. J.Rifà, On a Categorial Isomorphism between a class of Completely Regular Codes and a class of Distance Regular Graphs. Proceedings of AAECC-8. To appear in LNCS, Springer Verlag.

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  7. J.Rifà & J.Pujol, A Note on Completely Transitive Codes. Submmitted to Discrete Mathematics.

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  8. Patrick Solé, Completely Regular Codes and Completely Transitive Codes. North-Holland, Discrete Mathematics 81 (1990) 193–201.

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Author information

Authors and Affiliations

  1. Dpt. d'Informàtica, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Josep Rifà & Jaume Pujol

Authors
  1. Josep Rifà
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  2. Jaume Pujol
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Editor information

Harold F. Mattson Teo Mora T. R. N. Rao

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© 1991 Springer-Verlag Berlin Heidelberg

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Rifà, J., Pujol, J. (1991). Completely transitive codes and distance transitive graphs. In: Mattson, H.F., Mora, T., Rao, T.R.N. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1991. Lecture Notes in Computer Science, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54522-0_124

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  • DOI: https://doi.org/10.1007/3-540-54522-0_124

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54522-4

  • Online ISBN: 978-3-540-38436-6

  • eBook Packages: Springer Book Archive

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