The multiplicative complexity of symmetric functions over a field with characteristic p

In this thesis we consider the boolean elementary symmetric functions over a field with characteristic p, with p an odd, large enough prime. We will determine the coefficients of the symmetric functions. Also we will prove that it is possible to determine the coefficients with a recurrence relation of which the order depends on the number of variables of the degree of the smallest monomial in the symmetric polynomial. The multiplicative complexity of the symmetric polynomials is the number of multiplications needed to construct the polynomial. We will show the minimal number of multiplications needed for elementary symmetric functions with eight or less variables.