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Williamson matrices of orders 4·29 and 4·31

1992
*
Journal of combinatorial theory. Series A
*

It is established that there is only one,

doi:10.1016/0097-3165(92)90071-2
fatcat:ypnjih7kvzb53fkjeu5ruuhr4y
*up**to*equivalence,*Williamson*matrix of*order*4.29 and there are only two non-equivalent such*matrices*of*order*4.31. ... There exist five non-equivalent*Williamson**matrices*of*order*4.33 while only four of them are listed in [4] . ... For more details see our forthcoming paper "*Williamson**Matrices*of*Order*4n for n = 33, 35, 39" in Discrete Mathematics. is equivalent*to*the solution found byBaumert [ 11. ...##
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Applying Computer Algebra Systems with SAT Solvers to the Williamson Conjecture
[article]

2019
*
arXiv
*
pre-print

We find that, in contrast

arXiv:1804.01172v2
fatcat:nj2um7a7qzadbaa2om2ec3mr2a
*to*the case when the*order*is odd,*Williamson**matrices*of even*order*are quite plentiful and exist in every even*order**up**to*and including 70. ... As a consequence of this and a new construction for 8-*Williamson**matrices*we construct 8-*Williamson**matrices*in all odd*orders**up**to*and including 35. ... The authors thank Dragomir Ðoković informing us about the construction of Turyn (1970) using complex Hadamard*matrices*. ...##
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Supplementary difference sets with symmetry for Hadamard matrices
[article]

2009
*
arXiv
*
pre-print

Five new

arXiv:0903.5053v2
fatcat:nupvjb5ihfe5lcaiybp7kd7wve
*Williamson**matrices*over the elementary abelian groups of*order*25, 27 and 49 are constructed. New examples of skew Hadamard*matrices*of*order*4n for n=47,61,127 are presented. ... An old non-published example of G-*matrices*of*order*37 is also included. ... We refer*to*[11] for the*up*-*to*-date information on cyclic*Williamson**matrices*, including the complete listing of all nonequivalent such*matrices*of odd*order*≤*59*. ...##
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The SAT+CAS method for combinatorial search with applications to best matrices

2019
*
Annals of Mathematics and Artificial Intelligence
*

We show the best matrix conjecture (that best

doi:10.1007/s10472-019-09681-3
fatcat:paxe7oruzfeypf7cd2d6b75slu
*matrices*exist in all*orders*of the form r^2+r+1) which was previously known*to*hold for r≤6 also holds for r=7. ... Additionally, we apply the method*to*construct the largest best*matrices*yet known and present new skew Hadamard*matrices*constructed from best*matrices*. ... However, this approach was only able*to*find*Williamson**matrices*for*orders**up**to*n = 30. ...##
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Page 603 of Mathematical Reviews Vol. 50, Issue 3
[page]

1975
*
Mathematical Reviews
*

Currently,

*Williamson**matrices*are known*to*exist for all*orders*less than 100 except: 35, 39, 47, 53,*59*, 65, 67, 70, 71, 73, 76, 77, 83, 89, 94. ... Hadamard*matrices*of*order*less than 16 are unique*up**to*equivalence. There are just 5 equivalence classes for*order*16, 3 for*order*20 and at least 6 for*order*2" (n= 5). ...##
###
Page 5350 of Mathematical Reviews Vol. , Issue 92j
[page]

1992
*
Mathematical Reviews
*

Summary: “It is established that there is only one,

*up**to*equiv- alence,*Williamson*matrix of*order*4-29 and there are only two nonequivalent such*matrices*of*order*4-31.” 92j:05035 05B20 15A51 Hwang, ... )*Williamson**matrices*of*orders*4 - 29 and 4-31. ...##
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Page 1945 of Mathematical Reviews Vol. 49, Issue 6
[page]

1975
*
Mathematical Reviews
*

Hence Hadamard

*matrices*of*order*4wt and 20wt exist for the values of w and ¢ mentioned 49 #4/10575-10579 above, in particular for the*orders*4-*59*and 4-101, which were previously unknown. J. M. ... From a*Williamson*-type Hadamard matrix of*order*4w and a set of Baumert-Hall units of*order*4¢, a Hadamard matrix of*order*4wt can be constructed. ...##
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On Z_t ×Z_2^2-cocyclic Hadamard matrices
[article]

2014
*
arXiv
*
pre-print

In particular, these notions lead

arXiv:1112.4296v2
fatcat:p6ifxhdq7jfbvncv3cuhcdevjq
*to*the establishment of some bounds on the number and distribution of 2-coboundaries over Z_t ×Z _2^2*to*use and the way in which they have*to*be combined in*order**to*... Let H be the set of cocyclic Hadamard*matrices*over Z_t ×Z_2^2 having a symmetric diagram. We also prove that the set of*Williamson*type*matrices*is a subset of H of size | H|/t. ... ACKNOWLEDGMENTS The authors want*to*express their gratitude*to*the anonymous referees for their comments and suggestions, which have permitted*to*improve the readability and understandability of the paper ...##
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Symmetric Hadamard matrices of orders 268, 412, 436 and 604
[article]

2018
*
arXiv
*
pre-print

We construct many symmetric Hadamard

arXiv:1803.08787v1
fatcat:gc6evadp6zcebojd23xop3njr4
*matrices*of small*order*by using the so called propus construction. ... Our main result is that we have constructed, for the first time, symmetric Hadamard*matrices*of*order*268, 412, 436 and 604. ... Acknowledgements The research of the first author leading*to*these results has received funding from the Ministry of Education and Science of the Russian Federation according*to*the project part of the ...##
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NEGAPERIODIC GOLAY PAIRS AND HADAMARD MATRICES

2015
*
Information and Control Systems
*

We investigate the construction of Hadamard (and weighing

doi:10.15217/issn1684-8853.2015.5.2
fatcat:pqwnhupsxjat7hvjdmvwwywp4u
*matrices*) from two negacyclic blocks (2N-type). The Hadamard*matrices*of 2N-type are equivalent*to*negaperiodic Golay pairs. ... We show that the Ito's conjecture about Hadamard*matrices*is equivalent*to*the conjecture that negaperiodic Golay pairs exist for all even lengths. ... The known series of four*Williamson**matrices*of odd*order*give rise*to*the series of NG-pairs. As an example, we have computed four quasi-*Williamson**matrices*of*order*35. ...##
###
Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings

1974
*
Journal of combinatorial theory. Series A
*

If a

doi:10.1016/0097-3165(74)90056-9
fatcat:w4hnqh6fmvfrvgudj7vreqkdf4
*Williamson*matrix of*order*4w exists and a special type of design, a set of Baumert-Hall units of*order*4t, exists, then there exists a Hadamard matrix of*order*4tw. ... The constructions relate*to*various topics such as pulse compression and image encodings. 313 ... It seems very probable that there is some construction of Hadamard*matrices*of all*orders*4t which is very analogous*to*the*matrices*discussed here:*Williamson**matrices*exist of all*orders*4t fort,<31, ...##
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Higher dimensional orthogonal designs and applications

1981
*
IEEE Transactions on Information Theory
*

come

doi:10.1109/tit.1981.1056426
fatcat:bjmx4yar4vee3a5rbl2jz3ueyu
*to*be known as*Williamson**matrices*of side t. ... APPLYING ORTHOGONAL DESIGNS*TO*FORM HIGHER DIMENSIONAL HADAMARD*MATRICES**Williamson**matrices*of*order*t (or 4-suitable*matrices*in our present terminology) exist for the following*orders*(see [15[, [7 ...##
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Williamson theorem in classical, quantum, and statistical physics
[article]

2021
*
arXiv
*
pre-print

The objective of this text is

arXiv:2106.11965v1
fatcat:t45cqhati5gkjhcryiaaxj7r3e
*to*present (and encourage the use of) the*Williamson*theorem and its consequences in several contexts in physics. ... A modest introduction of the symplectic formalism in quantum mechanics is presented, which consequently opens*up*the use of the theorem*to*study quantum normal modes and quantum small oscillations, allowing ...*WILLIAMSON*THEOREM The question addressed by the*Williamson*theorem is the diagonalization of positive definite*matrices*through symplectic*matrices*. ...##
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Page 5273 of Mathematical Reviews Vol. , Issue 2001H
[page]

2001
*
Mathematical Reviews
*

Stanley Gill

*Williamson*(1-UCSD-CS; La Jolla, CA) 2001h:05015 05A15 33B10 Johnson, Warren P. (1-PAS; University Park, PA) Some polynomials associated with*up*-down permutations. ... The identity ch(F,) = ch(U,) of both characteristics is a consequence of S-MT, and is equivalent*to*a result of*Williamson*. ...##
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Some new operations on Zt x Z2,2-cocyclic Hadamard matrices
[article]

2014
*
arXiv
*
pre-print

These operations will be defined on the set of coboundaries defining the matrix, preserve the Hadamard character of the cocyclic

arXiv:1112.4300v2
fatcat:ruyuuufb7jeqtgzfivk3afnec4
*matrices*, and allow us*to*obtain new Hadamard*matrices*from old ones. ... We split the set of Hadamard*matrices*into disjoint orbits, define representatives for them and take advantage of this fact*to*compute them in an easier way than the usual purely exhaustive way. ... • The result about*Williamson**matrices*allows us*to*go beyond t = 23. ...
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