Title :
Generalized Bent Criteria for Boolean Functions (I)
Author :
Riera, Constanza ; Parker, Matthew G.
Author_Institution :
Fac. de Matematicas, Univ. Complutense de Madrid
Abstract :
Generalizations of the bent property of a Boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic Boolean functions are related to simple graphs and it is shown that the orbit generated by successive local complementations on a graph can be found within the transform spectra under investigation. The flat spectra of a quadratic Boolean function are related to modified versions of its associated adjacency matrix
Keywords :
Boolean functions; graph theory; matrix algebra; spectral analysis; associated adjacency matrix; generalized bent criteria; local unitary transform; quadratic Boolean function; spectral analysis; Boolean functions; Codes; Councils; Cryptography; Graph theory; Kernel; Quantum mechanics; Scholarships; Spectral analysis; Tensile stress; Additive codes; Boolean functions; Clifford group; Pauli group; bent functions; cryptography; graph states; graph theory; local complementation; quantum codes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.880069
