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On completely regular propelinear codes

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 357))

Abstract

In a previous paper (see [7]) we found that given a distance regular e-latticed graph γ we can associate with it a completely regular code C. We used this in order to solve a conjecture given by Bannai in [1].

In the present paper we introduce the propelinear code structure with the aim of studying the algebraic structure of completely regular codes (not necessarily linear) associated with distance-regular e-latticed graphs.

We give the basic properties of this structure. We construct, from a propelinear code C, an associate graph Ω(C) and we prove that C is a completely regular code if and only if Ω(C) is a distance-regular graph.

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References

  1. E. BANNAI & T. ITO, "Algebraic Combinatorics I". The Benjamin-Cummings Publishing Co., Inc. California. (1984).

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  2. P. DELSARTE, "An algebraic approach to the association schemes of coding theory". Philips Research Reps. Suppl. 10. (1973).

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  3. G. ETIENNE, "Perfect Codes and Regular Partition in Graphs and Groups". Europ. J. of Comb, 8, pp. 139–144 (1987).

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  5. J.RIFÀ, "Equivalències entre estructures combinatòricament regulars: Codis, Esquemes i grafs". Tesi doctoral. Univ. Autònoma de Barcelona. (1987).

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  6. J.RIFÀ & L. HUGUET, "Characterization of Completely Regular Codes through P-Polynomial Association Schemes". Springer-Verlag, LNCS, n. 307, 157–167, (1988).

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  7. J. RIFÀ & L. HUGUET, Classification of a Class of Distance-Regular Graphs via Completely Regular Codes. Proceed. CO87. Southampton 1987. To appear in Discrete Maths.

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Authors and Affiliations

  1. Dep.d'Informàtica. Fac. Ciències., Universitat Autònoma de Barcelona, Catalunya, Spain

    J. Rifà, J. M. Basart & L. Huguet

Authors
  1. J. Rifà
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  2. J. M. Basart
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  3. L. Huguet
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Editor information

Teo Mora

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© 1989 Springer-Verlag Berlin Heidelberg

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Rifà, J., Basart, J.M., Huguet, L. (1989). On completely regular propelinear codes. In: Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1988. Lecture Notes in Computer Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51083-4_71

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  • DOI: https://doi.org/10.1007/3-540-51083-4_71

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51083-3

  • Online ISBN: 978-3-540-46152-4

  • eBook Packages: Springer Book Archive

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