Propagation characteristics of Boolean functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Orphan structure of the first-order Reed-Muller codes
Discrete Mathematics
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the Orphans and Covering Radius of the Reed-Muller Codes
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Results on algebraic immunity for cryptographically significant boolean functions
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
On the norm and covering radius of the first-order Reed-Muller codes
IEEE Transactions on Information Theory
On some cosets of the first-order Reed-Muller code with high minimum weight
IEEE Transactions on Information Theory
Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros
Designs, Codes and Cryptography
On the lower bounds of the second order nonlinearities of some Boolean functions
Information Sciences: an International Journal
9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class
Information and Computation
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Z4-Nonlinearity of a constructed quaternary cryptographic functions class
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
A recursive formula for weights of Boolean rotation symmetric functions
Discrete Applied Mathematics
Weights of Boolean cubic monomial rotation symmetric functions
Cryptography and Communications
Results on rotation-symmetric S-boxes
Information Sciences: an International Journal
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The existence of 9-variable Boolean functions having nonlinearity strictly greater than 240 has been shown very recently (May 2006) by Kavut, Maitra and Yücel; a few functions with nonlinearity 241 have been identified by a heuristic search in the class of Rotation Symmetric Boolean Functions (RSBFs). In this paper, using combinatorial results related to the Walsh spectra of RSBFs, we efficiently perform the exhaustive search to enumerate the 9-variable RSBFs having nonlinearity 240 and found that there are 8 ×189 many functions with nonlinearity 241 and there is no RSBF having nonlinearity 241. We further prove that among these functions, there are only two which are different up to the affine equivalence. This is found by utilizing the binary nonsingular circulant matrices and their variants. Finally we explain the coding theoretic significance of these functions. This is the first time orphan cosets of R(1, n) having minimum weight 241 are demonstrated for n = 9. Further they provide odd weight orphans for n = 9; earlier these were known for certain n ≥11.