Cryptographically significant Boolean functions with five valued Walsh spectra
Theoretical Computer Science
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Evolving Boolean Functions Satisfying Multiple Criteria
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Further Results on the Relation Between Nonlinearity and Resiliency for Boolean Functions
Proceedings of the 7th IMA International Conference on Cryptography and Coding
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
Enumeration of 9-variable rotation symmetric boolean functions having nonlinearity 240
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
| Hi-index | 754.84 |
Let ρ(1,m) and N(1,m) be the covering radius and norm of the first-order Reed-Muller code R(1,m), respectively. It is known that ρ(1,2k+1)⩽lower bound [22k-2(2k-1/2)] and N(1,2k+1)⩽2 lower bound [22k-2(2k-1/2)] (k>0). We prove that ρ(1,2k+1)⩽2 lower bound [22k-1-2(2k-3/2)] and N(1,2k+1)⩽4 lower bound [22k-1-2(2k-3/2)] (k>0). We also discuss the connections of the two new bounds with other coding theoretic problems