Cocyclic Generalised Hadamard Matrices and Central RelativeDifference Sets
Designs, Codes and Cryptography
Hadamard and Conference Matrices
Journal of Algebraic Combinatorics: An International Journal
A New Construction of Central Relative (pa, pa, pa, 1)-Difference Sets
Designs, Codes and Cryptography
On Circulant Complex Hadamard Matrices
Designs, Codes and Cryptography
An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The homological reduction method for computing cocyclic Hadamard matrices
Journal of Symbolic Computation
On the asymptotic existence of cocyclic Hadamard matrices
Journal of Combinatorial Theory Series A
Rooted Trees Searching for Cocyclic Hadamard Matrices over D4t
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A heuristic procedure with guided reproduction for constructing cocyclic Hadamard matrices
ICANNGA'09 Proceedings of the 9th international conference on Adaptive and natural computing algorithms
On an inequivalence criterion for cocyclic Hadamard matrices
Cryptography and Communications
The cocyclic Hadamard matrices of order less than 40
Designs, Codes and Cryptography
Divisible designs and semi-regular relative difference sets from additive Hadamard cocycles
Journal of Combinatorial Theory Series A
A genetic algorithm for cocyclic hadamard matrices
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Calculating cocyclic hadamard matrices in mathematica: exhaustive and heuristic searches
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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We present the basic theory of cocyclic development of designs, in which group development over a finite group G is modified by the action of a cocycle defined on G × G. Negacyclic and ω-cyclic development are both special cases of cocyclic development.Techniques of design construction using the group ring, arising from difference set methods, also apply to cocyclic designs. Important classes of Hadamard matrices and generalized weighing matrices are cocyclic.We derive a characterization of cocyclic development which allows us to generate all matrices which are cocyclic over G. Any cocyclic matrix is equivalent to one obtained by entrywise action of an asymmetric matrix and a symmetric matrix on a G-developed matrix. The symmetric matrix is a Kronecker product of back ω-cyclic matrices, and the asymmetric matrix is determined by the second integral homology group of G.We believe this link between combinatorial design theory and low-dimensional group cohomology leads to (i) a new way to generate combinatorial designs; (ii) a better understanding of the structure of some known designs; and (iii) a better understanding of known construction techniques.