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

In this paper we present the weight distribution of all 2²6 cosets of the (32, 6) first-order Reed-Muller code. The code is invariant under the complete affine group, of order 32 31 30 28 24 16. In the Appendix we show (by hand computations) that this group partitions the 2²6 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 2³2 Boolean functions of five variables approximated by the 2⁵ linear functions and their complements?