Hadamard Matrices and Their Designs: A Coding-Theoretic Approach

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Abstract
To every finite dimensional algebraic coefficient system (defined below) over the De Rham algebra of a manifold , Sullivan builds a local system , in the topological sense, such that the two cohomologies and are isomorphic. In this paper, if is a simplicial set and an algebraic system over the forms , we prove a similar result. We use it to extend the Hirsch lemma to the case of fibration whose fiber is an Eilenberg-Mac Lane space with certain non nilpotent action of the fundamental group of the basis. We apply this to a model of the hyperbolic torus; different from the nilpotent one, this new model is a better mirror of the topology.

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