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Abstract. This paper presents an efficient approach to the classification of the affine equivalence classes of cosets of the first order ReedMuller code with respect to cryptographic properties such as correlationimmunity, resiliency and propagation characteristics. First, we apply the method to completely classify with this respect all the 48 classes into which the general affine group AGL(2, 5) partitions the cosets of RM (1, 5). Second, after distinguishing the 34 affine equivalence classes of cosets of RM (1, 6) in RM (3, 6) we perform the same classification for these classes.

Let Rt,n denote the set of t-resilient Boolean functions of n variables, and letρ(t, r, n) be the maximum distance between t-resilient functions and r-th order Reed-Muller code RM (r, n). We prove (analytically) thatρ(t, 2, 6) = 16 for t = 0, 1, 2,ρ(3, 2, 7) = 32. Using a result from coding theory on the covering radius of (n−3)-rd order Reed-Muller codes, we establish exact values of the covering radius of RM (n − 3, n) in the set of 1-resilient Boolean functions of n variables, when n/2 = 1 mod 2. We also present new lower bounds forρ(t, 2, 7) with t = 0, 1, 2, and generalize our methods to obtain lower bounds forρ(t, 2, n) with t ≤ n − 4,ρ(t, 3, n) with t ≤ n − 5, andρ(t, 4, n) with t ≤ n − 6.