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Mattson-Solomon transform and Gröbner bases : applications to association schemes and codes

The Mattson-Solomon transform of a semisimple algebra has been a valuable tool both in the theory of commutative association schemes and coding theory. In this talk we will review the relation between the structure of the Gröbner bases associated to these structures and some properties of the semisimple algebra related to the combinatorics of association schemes and codes.