A constructive count of rotation symmetric functions
Information Processing Letters
Note: On the weight and nonlinearity of homogeneous rotation symmetric Boolean functions of degree 2
Discrete Applied Mathematics
9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class
Information and Computation
Affine equivalence for rotation symmetric Boolean functions with 2k variables
Designs, Codes and Cryptography
Modifications of Patterson-Wiedemann functions for cryptographic applications
IEEE Transactions on Information Theory
The covering radius of the Reed-Muller code is at least 16276
IEEE Transactions on Information Theory
Search for Boolean Functions With Excellent Profiles in the Rotation Symmetric Class
IEEE Transactions on Information Theory
Affine equivalence of cubic homogeneous rotation symmetric functions
Information Sciences: an International Journal
Affine equivalence of quartic homogeneous rotation symmetric Boolean functions
Information Sciences: an International Journal
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Rotation symmetric Boolean functions, that is, Boolean functions which are invariant under any cyclic permutation of the variables, have been extensively studied in the last dozen years or so due to their importance in cryptography and coding theory. Little was known about the basic question of when two such functions are affine equivalent until very recently. The case of affine equivalence of quadratic rotation symmetric functions was solved in 2009 by Kim, Park and Hahn. In 2010, Cusick introduced the concept of patterns to study the more complicated case of cubic functions under permutations. This method made possible a detailed analysis of some special classes of cubic rotation symmetric functions in n variables where n has a special form, for example, n equal to a prime power. Here the affine equivalence classes under permutations in n variables for any n are examined. In particular, all possible sizes of these classes are identified and an exact count of the functions in the largest classes is given. It is conjectured that the classes of the largest size contain a positive proportion of all of the distinct functions in n variables.