TL;DR
This paper explores the connection between linear codes and graphical designs on cube graphs, highlighting the Hamming code as an effective example and distinguishing graphical designs from related combinatorial concepts.
Contribution
It establishes a link between linear codes and graphical designs on cube graphs and demonstrates the unique properties of these designs compared to similar concepts.
Findings
Hamming code is a highly effective graphical design
Graphical designs differ from extremal designs and maximum stable sets
Connections between codes and designs on cube graphs are established
Abstract
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that even in highly structured graphs, graphical designs are distinct from the related concepts of extremal designs, maximum stable sets in distance graphs, and -designs on association schemes.
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