Geodesic
Cocyclic development of designs
Journal of Algebraic Combinatorics, Tome 2 (1993) no. 3, pp. 267-290.

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Summary: 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 $G \times G.$ Negacyclic and $ohgr$-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.
Classification : 05B10,, 05B15,, 05B20,, 20J06
Keywords: orthogonal design, Hadamard matrix, difference set, group development, negacyclic development, $ohgr$-cyclic development, cocycle, cohomology group, homology group, extension group 
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     author = {Horadam, K.J. and de Launey, W.},
     title = {Cocyclic development of designs},
     journal = {Journal of Algebraic Combinatorics},
     pages = {267--290},
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     year = {1993},
     language = {en},
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Horadam, K.J.; de Launey, W. Cocyclic development of designs. Journal of Algebraic Combinatorics, Tome 2 (1993) no. 3, pp. 267-290. http://geodesic.mathdoc.fr/item/JAC_1993__2_3_a1/