On completely regular propelinear codes | SpringerLink
Skip to main content
Springer Nature Link
Log in

On completely regular propelinear codes

  • Full Papers
  • Conference paper
  • First Online:
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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  4. D.G. HIGMAN, "Coherent Configuration I Ordinary Representation Theory". Geom. Dedic. 4, pp. 1–32 (1975).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  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.

    Google Scholar 

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Basart
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Huguet
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Teo Mora

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51083-3

  • Online ISBN: 978-3-540-46152-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation