Designs, Codes and Cryptography
Cryptographically significant Boolean functions with five valued Walsh spectra
Theoretical Computer Science
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A New Characterization of Semi-bent and Bent Functions on Finite Fields*
Designs, Codes and Cryptography
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Generalized construction of binary bent sequences with optimal correlation property
IEEE Transactions on Information Theory
New classes of almost bent and almost perfect nonlinear polynomials
IEEE Transactions on Information Theory
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The construction method of bent-function sequences is generalized to construct sequences with low correlation from functions with low maximal Walsh transform. In detail, for any nonlinear function from $F_{2^e}^{k}$ to F 2 with maximum magnitude spectra A , a family of sequences with period 22ek *** 1 can be constructed. There are 2 ek sequences within a family and the maximum nontrival auto and cross-correlation values equals A 2 + 1. The linear span of these proposed sequences is discussed and the lower bound can be greater than $\left(\begin{array}{cc}ek\\d\end{array}\right)2^{d}+2ek$, where 2 ≤ d ek .