Abstract
A code in a graph Γ is a non-empty subset C of the vertex set V of Γ. Given C, the partition of V according to the distance of the vertices away from C is called the distance partition of C. A completely regular code is a code whose distance partition has a certain regularity property. A special class of completely regular codes are the completely transitive codes. These are completely regular codes such that the cells of the distance partition are orbits of some group of automorphisms of the graph. This paper looks at these codes in the Hamming Graphs and provides a structure theorem which shows that completely transitive codes are made up of either transitive or nearly complete, completely transitive codes. The results of this paper suggest that particular attention should be paid to those completely transitive codes of transitive type.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
