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Cocyclic Orthogonal Designs and the Asymptotic Existence of Cocyclic Hadamard Matrices and Maximal Size Relative Difference Sets with Forbidden Subgroup of Size 2
2001
Journal of combinatorial theory. Series A
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Then there is a normal relative difference set of size 2 t s with forbidden subgroup (z) in the group T_S." ...
This paper contains a discussion of cocyclic Hadamard matrices, their associated relative difference sets, and regular group actions. ...
We use the notation NRDS(v, k, *, m) to denote a normal relative difference set of size k in a group of size v with forbidden subgroup of size m and index *. ...
doi:10.1006/jcta.2000.3062
fatcat:hycctamiobfmxnozq2s5jgowte
Page 47 of Mathematical Reviews Vol. , Issue 2002A
[page]
2002
Mathematical Reviews
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Cocyclic orthogonal designs and the asymptotic existence of cocyclic Hadamard matrices and maximal size relative difference sets with forbidden subgroup of size 2. (English summary)
J. Combin. ...
The authors note that Dg does not contain any relative (4, 2,4, 2)- difference set relative to a normal subgroup of order 2, though it does contain such an RDS relative to a nonnormal one
The proof uses ...
Page 873 of Mathematical Reviews Vol. , Issue 2001B
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2001
Mathematical Reviews
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Smith, “Cocyclic orthogonal designs and the asymptotic existence of maximal size relative difference sets with forbidden subgroup size 2”, Preprint, 1998; per bibl.]). ...
However, there exist relative (4, 2, 41, 2t)-difference sets relative to nonnormal subgroups of order 2, in groups which have no central RDS with these parameters (for example Dg [W. de Launey and M. ...
On the asymptotic existence of cocyclic Hadamard matrices
2009
Journal of combinatorial theory. Series A
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We also show that if the binary expansion of q contains N ones, then there is a cocyclic Hadamard matrix of order 2 4N−2 q. ...
We prove there is a cocyclic Hadamard matrix of order 2 10+t q whenever t 8 log 2 (q−1) 10 . ...
Acknowledgments The authors thank the referees for their valuable help in the preparation of this article. ...
doi:10.1016/j.jcta.2009.03.002
fatcat:5cgvx6vbgvfvfbq4kwwsd3u5ei
Page 137 of Mathematical Reviews Vol. , Issue Subject Index
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Mathematical Reviews
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Cocyclic orthogonal designs and the asymptotic existence of cocyclic Hadamard matrices and maximal size relative difference sets with forbidden subgroup of size 2. ...
Cocyclic orthogonal designs and the asymptotic existence of cocyclic Hadamard matrices and maximal size relative difference sets with forbidden subgroup of size 2. ...
Invitation to Hadamard matrices
[article]
2022
arXiv
pre-print
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2021 pre-print arXiv:1910.06911v5 fatcat:czn6uho365hqvcaquf4pmwvu7qOther Versions
The main example is the Fourier matrix, F_N=(w^ij) with w=e^2π i/N. We discuss here the basic theory of such matrices, with emphasis on geometric and analytic aspects. ...
A complex Hadamard matrix is a square matrix H∈ M_N(ℂ) whose entries are on the unit circle, |H_ij|=1, and whose rows and pairwise orthogonal. ...
As a conclusion to this study, looking at the maximizers H ∈ M N (±1) of the quantity | det H| is not exactly an ideal method, when looking for analogues of the Hadamard matrices at the forbidden size ...
arXiv:1910.06911v6
fatcat:g6jbj5zerzbfzpagikjgs6bcoe
Page 1088 of Mathematical Reviews Vol. , Issue Author Index
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Mathematical Reviews
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Cocyclic orthogonal designs and the asymptotic existence of cocyclic Hadamard matrices and maximal size relative difference sets with forbidden subgroup of size 2. (English summary) J. Combin. ...
(Summary) 2002m:05036 05B05
— (with Magliveras, Spyros S.; Wassermann, Alfred) New large sets of t-designs. (English summary) J. Combin. Des. 9 (2001), no. 1, 40-59. ...
Page 1857 of Mathematical Reviews Vol. , Issue Author Index
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(with de Launey, Warwick) Cocyclic orthogonal designs and the asymptotic existence of cocyclic Hadamard matrices and maximal size relative difference sets with forbidden subgroup of size 2. ...
(with Adem, Alejandro) Periodic complexes and group actions. (English summary) Ann. of Math. (2) 154 (2001), no. 2, 407-435. ...
Transformation & Uncertainty. Some Thoughts on Quantum Probability Theory, Quantum Statistics, and Natural Bundles
[article]
2010
arXiv
pre-print
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of decoherence and the impossibility of perfect joint measurement. ...
We then propose a two-step strategy to determine the (possibly mixed) state of n identically prepared qubits, and prove that it is asymptotically optimal in a local minimax sense, using 'Quantum Local ...
Two Lemmas We set out to prove theorem 7.23. We start with two lemmas designed to explicate the homomorphism ρ : G(k, M ) → GL(R n ) × Z G. ...
arXiv:1011.3035v1
fatcat:zgpqhl75tndttdyngxxubasyqy
Lyapunov Exponents in the Spectral Theory of Primitive Inflation Systems
2019
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In this work, we consider primitive inflation rules as generators of aperiodic tilings, and subsequently, of aperiodic point sets (which are toy models for quasicrystals) deemed adequate for diffraction ...
We show that this holds for large classes of systems, and, as a sanity check, show that the necessary criterion for existence is satisfied by systems which are a priori known to have absolutely continuous ...
Instead, we take advantage of the five-fold symmetry of a GLB tiling and work with a different set of generators. ...
doi:10.4119/unibi/2935972
fatcat:nfzju7dagzemdn3pkrra3frcji
Toward a Generalized Shapiro and Shapiro Conjecture
[chapter]
2011
PROGRESS IN MATHEMATICS
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Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. ...
On the Content of This Volume xvii the fact that rational unknots in tight contact structures on lens spaces are weakly transversely simple and Legendrian simple. ...
He extends his special thanks to Ilia Itenberg, Burglind Jöricke, and Mikael Passare, the editors of these proceedings, for their patience with the author. ...
doi:10.1007/978-0-8176-8277-4_4
fatcat:jh7utclvbve43ja7pghc6bp3fi
A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas Compiled by
1996
unpublished
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Generalizations of § §3, 4 are sketched and are applied to find the number of H-equivalent matrices of given size with entries ±1, ±1, . . . , ±k. ...
There exist pairs of unbalanced, strictly quasicospectral graphs; existence of larger sets is unsolved. ...
The property is the existence of an Eulerian cut. The asymptotic probability is .57 . . .. [Problem. Generalize to gain graphs with finite gain group, esp. to signed graphs. ...
fatcat:os5lveptfbbbplmcy4drb2zd3m