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The cocyclic Hadamard matrices of order less than 40
TLDR
All cocyclic Hadamard matrices of order less than 40 are classified, which represents a significant extension and completion of work by de Launey and Ito and involves a complete enumeration and construction of (4t, 2, 4T, 2t)-relative difference sets in the groups of orders 64 and 72. Expand
On twin prime power Hadamard matrices
TLDR
This work answers a research problem posed by K.J. Horadam, and exhibits the first known infinite family of Hadamard matrices which are not cocyclic, by showing that the action of the automorphism group of a hadamard matrix developed from a difference set induces a 2-transitive action on the rows of the matrix. Expand
Explicit correlation amplifiers for finding outlier correlations in deterministic subquadratic time
TLDR
The derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiant's randomized algorithm, but the precise constants the authors save over quadratic scaling are more modest. Expand
Automorphisms of Pairwise Combinatorial Designs
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Inequivalence of Difference Sets: On a Remark of Baumert
TLDR
An often cited statement of Baumert that four well known families of cyclic difference sets are inequivalent is extended to a general inequivalence result, for which a complete and self-contained proof is provided. Expand
Spectra of Hadamard matrices
TLDR
A technique for controlling the spectra of certain Hadamard matrices is developed, generalising a well-known result of Turyn. Expand
Compressed sensing and designs: theory and simulations
TLDR
This paper analyses the performance of a new construction for compressed sensing matrices using deterministic and probabilistic methods and provides a new recovery algorithm and detailed simulations that suggest the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. Expand
Homomorphisms of matrix algebras and constructions of Butson-Hadamard matrices
TLDR
It is proved that if $k = mt$, and each prime divisor of $k$ divides $t$, then one can construct a matrix H' in BH(mn, t) from any $H \in BH (n,k)$. Expand
Difference sets and doubly transitive actions on Hadamard matrices
TLDR
This work classify all difference sets which give rise to Hadamard matrices with non-affine doubly transitive automorphism group, and uncovers a new triply infinite family of skew-Hadamard difference sets in non-abelian p-groups with no exponent restriction. Expand
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