On completely regular propelinear codes
In a previous paper (see ) 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 .
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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