Neighbour transitivity on codes in Hamming graphs

Details Neighbour transitivity on codes in Hamming graphs Neighbour transitivity on codes in Hamming graphs

2011-12-06

arxiv.org/abs/1112.1244v1

Mathematics

Combinatorics

Scientific paper

We consider a \emph{code} to be a subset of the vertex set of a \emph{Hamming graph}. In this setting a \emph{neighbour} of the code is a vertex which differs in exactly one entry from some codeword. This paper examines codes with the property that some group of automorphisms acts transitively on the \emph{set of neighbours} of the code. We call these codes \emph{neighbour transitive}. We obtain sufficient conditions for a neighbour transitive group to fix the code setwise. Moreover, we construct an infinite family of neighbour transitive codes, with \emph{minimum distance} $\delta=4$, where this is not the case. That is to say, knowledge of even the complete set of code neighbours does not determine the code.

Affiliated with

Also associated with

No associations

Rating

Neighbour transitivity on codes in Hamming graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Neighbour transitivity on codes in Hamming graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Neighbour transitivity on codes in Hamming graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380972