On Perfect Codes in the Johnson Graph
Natalia Silberstein, Tuvi Etzion
TL;DR
This paper investigates the existence of perfect codes in Johnson graphs, using combinatorial and number theory methods to establish necessary conditions and narrow down possible parameters for such codes.
Contribution
It introduces new combinatorial and number theory techniques to determine necessary conditions for perfect codes in Johnson graphs, reducing the parameter space for their existence.
Findings
Identified necessary conditions for 1-perfect and 2-perfect codes in Johnson graphs.
Reduced the range of parameters where such codes could exist.
Provided a framework for further exploration of perfect codes in combinatorial structures.
Abstract
In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n,w). We present combinatorial and number theory techniques to provide necessary conditions for existence of such codes and reduce the range of parameters in which 1-perfect and 2-perfect codes may exist.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Cellular Automata and Applications