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I wanted to find out what are some application of SGT in the area of information and coding theory and maybe communications. The most related that comes to mind is the work on Expander Codes

Michael Sipser and Daniel Spielman, "Expander Codes", IEEE Transactions on Information Theory, Vol 42, No 6, pp. 1710-1722. 1996

Other examples?

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Cayley graphs of codes and derandomized code products can be a good example. See the following thesis (Chapter 6) for details and references: http://library.epfl.ch/en/theses/?nr=3816

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Lovasz theta number of a graph is defined through spectral techniques.

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