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We show that the weight enumerator of any binary linear code is equal to thepermanent of a 3-dimensional hypermatrix (3-matrix). We also show that eachpermanent is a determinant of a 3-matrix. As an application we write the dimerpartition function of a finite 3-dimensional cubic lattice as the determinantof the vertex-adjacency 3-matrix of a 2-dimensional simplicial complex whichpreserves the natural embedding of the cubic lattice.

Binary Linear Codes, Dimers and Hypermatrices