Applied combinatorics
Orphan structure of the first-order Reed-Muller codes
Discrete Mathematics
Rotation symmetric Boolean functions-Count and cryptographic properties
Discrete Applied Mathematics
Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros
Designs, Codes and Cryptography
Improved fast correlation attacks using parity-check equations of weight 4 and 5
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Enumeration of 9-variable rotation symmetric boolean functions having nonlinearity 240
INDOCRYPT'06 Proceedings of the 7th 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
Weight distributions of the cosets of the (32,6) Reed-Muller code
IEEE Transactions on Information Theory
On the covering radius of binary codes (Corresp.)
IEEE Transactions on Information Theory
The covering radius of the (128,8) Reed-Muller code is 56 (Corresp.)
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
Weights of Boolean cubic monomial rotation symmetric functions
Cryptography and Communications
Results on rotation-symmetric S-boxes
Information Sciences: an International Journal
Equivalence classes for cubic rotation symmetric functions
Cryptography and Communications
Affine equivalence of quartic homogeneous rotation symmetric Boolean functions
Information Sciences: an International Journal
| Hi-index | 0.00 |
We give a new lower bound to the covering radius of the first order Reed-Muller code RM(1,n), where n@?{9,11,13}. Equivalently, we present the n-variable Boolean functions for n@?{9,11,13} with maximum nonlinearity found till now. In 2006, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel. To improve this nonlinearity result, we have firstly defined some subsets of the n-variable Boolean functions as the generalized classes of ''k-RSBFs and k-DSBFs (k-Dihedral Symmetric Boolean Functions)'', where k is a positive integer dividing n. Secondly, utilizing a steepest-descent like iterative heuristic search algorithm, we have found 9-variable Boolean functions with nonlinearity 242 within the classes of both 3-RSBFs and 3-DSBFs. Thirdly, motivated by the fact that RSBFs are invariant under a special permutation of the input vector, we have classified all possible permutations up to the linear equivalence of Boolean functions that are invariant under those permutations.