Szemerédi Endre: Struktura es véletlenszerűség

Let V be a finite dimensional vector space over the field F with two elements. Assume that we are given a nondegenerate symplectic form on V with values in F. Let V^C be the C-vector space of complex valued functions on V. Fourier transform Is a linear isomorphism from V^C to V^C. We will construct a remarkable basis of V^C in which Fourier transform acts as a triangular matrix. This is somewhat similar to an old result of Hermite about diagonalizing the usual Fourier transform over real numbers.