Matrix analysis
Design theory
Differentially uniform mappings for cryptography
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Planar Functions and Planes of Lenz-Barlotti Class II
Designs, Codes and Cryptography
Journal of Complexity - Special issue on coding and cryptography
Picturing qubits in phase space
IBM Journal of Research and Development
A family of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
Nonlinear functions in abelian groups and relative difference sets
Discrete Applied Mathematics
Generalized Welch bound equality sequences are tight frames
IEEE Transactions on Information Theory
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The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for a system of vectors to satisfy the Welch bounds with equality is given and applied for the case of MUBs. This yields a necessary and sufficient condition on a set of orthonormal bases to form a complete system of MUBs. This condition takes an especially elegant form in the case of homogeneous systems of MUBs. We express some known constructions of MUBs in this form. Also it is shown how recently obtained results binding MUBs and some combinatorial structures (such as perfect nonlinear functions and relative difference sets) naturally follow from this criterion. Some directions for proving non-existence results are sketched as well.