Weight distributions of the cosets of the (32,6) Reed-Muller code

In this paper we present the weight distribution of all 2^26 cosets of the (32,6) first-order Reed-Muller code. The code is invariant under the complete affine group, of order 32 \times 31 \times 30 \times 28 \times 24 \times 16. In the Appendix we show (by hand computations) that this group partitions the 2^26 cosets into only 48 equivalence classes, and we obtain the number of cosets in each class. A simple computer program then enumerated the weights of the 32 vectors ih each of the 48 cosets. These coset enumerations also answer this equivalent problem: how well are the 2^32 Boolean functions of five variables approximated by the 2^5 linear functions and their complements?