# On completely regular propelinear codes

• J. Rifà
• J. M. Basart
• L. Huguet
Full Papers
Part of the Lecture Notes in Computer Science book series (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

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E. BANNAI & T. ITO, "Algebraic Combinatorics I". The Benjamin-Cummings Publishing Co., Inc. California. (1984).Google Scholar
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G. ETIENNE, "Perfect Codes and Regular Partition in Graphs and Groups". Europ. J. of Comb, 8, pp. 139–144 (1987).Google Scholar
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J.RIFÀ, "Equivalències entre estructures combinatòricament regulars: Codis, Esquemes i grafs". Tesi doctoral. Univ. Autònoma de Barcelona. (1987).Google Scholar
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J.RIFÀ & L. HUGUET, "Characterization of Completely Regular Codes through P-Polynomial Association Schemes". Springer-Verlag, LNCS, n. 307, 157–167, (1988).Google Scholar
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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

© Springer-Verlag Berlin Heidelberg 1989

## Authors and Affiliations

• J. Rifà
• 1
• J. M. Basart
• 1
• L. Huguet
• 1
1. 1.Dep.d'Informàtica. Fac. Ciències.Universitat Autònoma de BarcelonaCatalunyaSpain