The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Codes, Bent Functions and Permutations Suitable For DES-likeCryptosystems
Designs, Codes and Cryptography
Upper and Lower Bounds on Maximum Nonlinearity ofn-input m-output Boolean Function
Designs, Codes and Cryptography
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
On the construction of highly nonlinear permutations
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
New families of quadratic almost perfect nonlinear trinomials and multinomials
Finite Fields and Their Applications
Finite Fields and Their Applications
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In this paper we give a new construction of highly nonlinear vectorial Boolean functions. This construction is based on coding theory, more precisely we use concatenation to construct Boolean functions from codes over $\mathbb{F}_q$ containing a first-order generalized Reed---Muller code. As it turns out this construction has a very compact description in terms of Boolean functions, which is of independent interest. The construction allows one to design functions with better nonlinearities than known before.