On maximal cliques in the graph of simplex codes
Mariusz Kwiatkowski, Mark Pankov
TL;DR
This paper investigates the structure of maximal cliques within the graph formed by simplex codes in the Grassmann graph, revealing two distinct types and their automorphisms, which enhances understanding of their combinatorial properties.
Contribution
The paper identifies and characterizes two types of maximal cliques in the Grassmann graph of simplex codes, including automorphism properties of the first type.
Findings
Two types of maximal cliques identified
Automorphisms relate cliques of the first type
Complexity varies among second type cliques
Abstract
The induced subgraph of the corresponding Grassmann graph formed by simplex codes is considered. We show that this graph, as the Grassmann graph, contains two types of maximal cliques. For any two cliques of the first type there is a monomial linear automorphism transferring one of them to the other. Cliques of the second type are more complicated and can contain different numbers of elements.
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Taxonomy
TopicsCoding theory and cryptography · Graph Labeling and Dimension Problems · Cooperative Communication and Network Coding