Codes, Cubes, and Graphical Designs
Combinatorics
2021-07-22 v4 Discrete Mathematics
Spectral Theory
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.
Cite
@article{arxiv.2012.12376,
title = {Codes, Cubes, and Graphical Designs},
author = {Catherine Babecki},
journal= {arXiv preprint arXiv:2012.12376},
year = {2021}
}
Comments
31 pages, 12 figures, 3 tables. To appear in the Journal of Fourier Analysis and Applications, Special Issue "Harmonic Analysis on Graphs", 2021