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The shift action on 2-cocycles. (English) Zbl 1043.20026
This paper is a very interesting one at least for the applications concerning representation theory, combinatorial design and quantum dynamics. Introducing shift actions from a group \(G\) on the group of 2-cocycles from \(G \) to an Abelian group \(C\), there are obtained stronger equivalence relations than does cohomology. In the last section there is also given a very nice application to digital signal design.

20J06 Cohomology of groups
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
94A60 Cryptography
Full Text: DOI
[1] Aschbacher, M., Finite group theory, (1993), Cambridge University Press Cambridge · Zbl 0826.20001
[2] Blokhuis, A.; Jungnickel, D.; Schmidt, B., Proof of the prime power conjecture for projective planes of order n with abelian collineation groups of order n2, Proc. amer. math. soc., 130, 1473-1476, (2002) · Zbl 1004.51012
[3] Brown, K.S., Cohomology of groups, Graduate text in mathematics, Vol. 87, (1982), Springer New York
[4] F. Chabaud, A. De Santis, S. Vaudenay, Links between linear and differential cryptanalysis, in: EUROCRYPT-94, Lecture Notes in Computer Science, Vol. 950, Springer, New York, 1995, pp. 356-365. · Zbl 0879.94023
[5] Flannery, D.L., Calculation of cocyclic matrices, J. pure appl. algebra, 112, 181-190, (1996) · Zbl 0867.20043
[6] Flannery, D.L., Cocyclic Hadamard matrices and Hadamard groups are equivalent, J. algebra, 192, 749-779, (1997) · Zbl 0889.05032
[7] K.J. Horadam, M. Fossorier, H. Imai, S. Lin, A. Poli, Sequences from cocycles, in: AAECC-13, Lecture Notes in Computer Science, Vol. 1719, Springer, Berlin, 1999, pp. 121-130.
[8] Horadam, K.J., Equivalence classes of central semiregular relative (v,w,v,v/w)-difference sets, J. combin. designs, 8, 330-346, (2000) · Zbl 0953.05009
[9] Horadam, K.J.; Udaya, P., Cocyclic Hadamard codes, IEEE trans. inform. theory, 46, 1545-1550, (2000) · Zbl 0994.94032
[10] Horadam, K.J.; Udaya, P., A new construction of central relative (pa,pa,pa,1)-difference sets, Design codes cryptogr., 27, 281-295, (2002) · Zbl 1027.05013
[11] Kerber, A., Applied finite group actions, (1999), Springer Berlin · Zbl 0951.05001
[12] Leung, K.H.; Ma, S.L.; Tan, V., Planar functions from \( Zn\) to \( Zn\), J. algebra, 224, 427-436, (2000)
[13] W.-H. Liu, Y.-Q. Chen, K.J. Horadam, Relative difference sets fixed by inversion (II)—character theoretical approach, preprint, 2002.
[14] Morandi, P., Field and Galois theory, Graduate text in mathematics, Vol. 167, (1996), Springer New York
[15] K. Nyberg, D.W. Davies, Perfect nonlinear S-boxes, in: EUROCRYPT-91, Lecture Notes in Computer Science, Vol. 547, Springer, New York, 1991, pp. 378-385. · Zbl 0766.94012
[16] K. Nyberg, T. Helleseth, Differentially uniform mappings for cryptography, in: EUROCRYPT-93, Lecture Notes in Computer Science, Vol. 765, Springer, New York, 1994, pp. 55-64. · Zbl 0951.94510
[17] Perera, A.A.I.; Horadam, K.J., Cocyclic generalised Hadamard matrices and central relative difference sets, Design codes cryptogr., 15, 187-200, (1998) · Zbl 0919.05007
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