Design theory
Spin models constructed from Hadamard matrices
Journal of Combinatorial Theory Series A
Finite fields
Discrete Mathematics
Mutually unbiased bases and orthogonal decompositions of Lie algebras
Quantum Information & Computation
Complex sequences with low periodic correlations (Corresp.)
IEEE Transactions on Information Theory
On the inequivalence of generalized Preparata codes
IEEE Transactions on Information Theory
On Weyl-Heisenberg orbits of equiangular lines
Journal of Algebraic Combinatorics: An International Journal
Semi-regular relative difference sets with large forbidden subgroups
Journal of Combinatorial Theory Series A
Close Encounters with Boolean Functions of Three Different Kinds
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
Bounds for codes and designs in complex subspaces
Journal of Algebraic Combinatorics: An International Journal
On the equivalence between real mutually unbiased bases and a certain class of association schemes
European Journal of Combinatorics
Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power
Cryptography and Communications
Unbiased complex Hadamard matrices and bases
Cryptography and Communications
Mutually unbiased bases and orthogonal decompositions of Lie algebras
Quantum Information & Computation
Galois automorphisms of a symmetric measurement
Quantum Information & Computation
Systems of imprimitivity for the clifford group
Quantum Information & Computation
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We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters (k,n,k,@l) we construct sets of n+1 mutually unbiased bases in C^k. We show how to construct these difference sets from commutative semifields and that all known maximal sets of mutually unbiased bases can be obtained in this way, resolving a conjecture about the monomiality of maximal sets. We also relate mutually unbiased bases to spin models.