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Screening Properties And Design Selection Of Certain Two-Level Designs

H. Evangelaras, Christos Koukouvinos
2003 Journal of Modern Applied Statistical Methods  
In this paper we give all the inequivalent projections of inequivalent Hadamard matrices of order 28 into k=3 and 4 dimensions and furthermore, we give partial results for k=5.  ...  Then, we sort these projections according to their generalized resolution and their generalized aberration.  ...  Inequivalent Hadamard matrices have different projection properties.  ... 
doi:10.22237/jmasm/1051747740 fatcat:txwohk5gina5xhwi6pa6asofcq

Robust Hadamard matrices, unistochastic rays in Birkhoff polytope and equi-entangled bases in composite spaces [article]

Grzegorz Rajchel, Adam Gąsiorowski, Karol Życzkowski
2018 arXiv   pre-print
We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a 2-dimensional subspace forms a Hadamard matrix.  ...  These unitary matrices allow us to construct a family of orthogonal bases in the composed Hilbert space of order n × n.  ...  Basic properties of robust Hadamard matrices One can easily see that the following Hadamard matrix of order four is robust and is equivalent to a skew Hadamard: H R 4 =     1 1 1 1 1 −1 −1 1 1 1 −1  ... 
arXiv:1804.10715v2 fatcat:rke2k6h65rcrrj6nvh7o6r3zge

Robust Hadamard Matrices, Unistochastic Rays in Birkhoff Polytope and Equi-Entangled Bases in Composite Spaces

Grzegorz Rajchel, Adam Gąsiorowski, Karol Życzkowski
2018 Mathematics in Computer Science  
We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a 2-dimensional subspace forms a Hadamard matrix.  ...  In the case n = 4 we study geometry of the set U4 of unistochastic matrices, conjecture that this set is star-shaped and estimate its relative volume in the Birkhoff polytope B4.  ...  Basic properties of robust Hadamard matrices One can easily see that the following Hadamard matrix of order four is robust and is equivalent to a skew Hadamard: H R 4 =     1 1 1 1 1 −1 −1 1 1 1 −1  ... 
doi:10.1007/s11786-018-0384-y fatcat:4czcwgt4brebpfoodod2w5uwmi

Page 5928 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
Summary: “We consider the projective properties of small Hadamard matrices when viewed as two-level orthogonal arrays of strength two.  ...  Then 16 x 16 checkered Hadamard matrices H and K are called block equivalent if there exist monomial matrices S and T with entries +1 and —1 (signed permutation matrices) such that SHT = K, SGT =G.  ... 

Page 2994 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
The five Hadamard matrices of size 16 and their associated codes are examined in detail. Also, the sixty Hadamard matrices of size 24 are partitioned into six 2-equivalence classes.  ...  among the latter designs only the one with A = 1 is equivalent to a Hadamard tournament.  ... 

ANOTHER LOOK AT NEW GMA ORTHOGONAL ARRAYS

Yingfu Li, Timothy Wittig
2001 Conference on Applied Statistics in Agriculture  
orthogona.l alTays. 117 In this paper, we study those top orthogonal arrays that cannot be embedded into Hadamard matrices from the angle of projection.  ...  Li, Deng, and Tang (2000) studied nOll-regular designs and generated a collection of non-equivalent orthogonal arrays using a generalized miniumm aberration criterion, proposed by Deng and Tang (1999)  ...  As we know that there are three non-equivalent Hadamard matrices of order 20 (Hall, 1965) .  ... 
doi:10.4148/2475-7772.1220 fatcat:53scwqcorvgjlmiacgl7ktkp5q

Page 5972 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
(GR-ATHN; Athens) On equivalence of Hadamard matrices and projection properties. (English summary) Ars Combin. 69 (2003), 79-95.  ...  “In this paper we use inequivalent projections of Hadamard matrices and their symmetric Hamming distances to check the inequivalence of Hadamard matrices.  ... 

Page 821 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Spencer P. (1-CITA; Charleston, SC); Sarvate, Dinesh G. (1-UCH; Charleston, SC) On c-Hadamard matrices.  ...  From the text: “One of the most outstanding problems in combi- natorial mathematics and geometry is the problem of existence of finite projective planes whose order is not a prime power.  ... 

Quantum Latin squares and unitary error bases [article]

Benjamin Musto, Jamie Vicary
2016 arXiv   pre-print
Our main results are on applications to unitary error bases (UEBs), basic structures in quantum information which lie at the heart of procedures such as teleportation, dense coding and error correction  ...  We show that our new approach simultaneously generalizes the shift-and-multiply and Hadamard methods.  ...  All Hadamard matrices on C 4 are equivalent to one of the following Fourier matrices, parameterised by α ∈ [0, π 2 ]: H α :=     1 1 1 1 1 1 −1 −1 1 −1 e iα −e iα 1 −1 −e iα e iα     ( Y := 1  ... 
arXiv:1504.02715v2 fatcat:i4bnxp2e35f5dn67v5f2jmxjxq

The quantum algebra of partial Hadamard matrices [article]

Teo Banica, Adam Skalski
2014 arXiv   pre-print
A partial Hadamard matrix is a matrix H∈ M_M× N( T) whose rows are pairwise orthogonal. We associate to each such H a certain quantum semigroup G of quantum partial permutations of {1,...  ...  We discuss as well the relation between the completion problems for a given partial Hadamard matrix and completion problems for the associated submagic matrix P∈ M_M(M_N( C)), in both cases introducing  ...  Acknowledgment: We would like to thank the referee for careful reading of our manuscript and several useful comments improving the presentation.  ... 
arXiv:1310.3855v3 fatcat:t6eqtpwv6jalnaovas3qe7drjm

Hadamard Matrices and Their Designs: A Coding-Theoretic Approach

E. F. Assmus, J. D. Key
1992 Transactions of the American Mathematical Society  
This leads naturally to the notion, defined for any prime p , of p-equivalence for Hadamard matrices for which the standard equivalence of Hadamard matrices is, in general, a refinement: for example, the  ...  We study these, and other classes of designs associated with Hadamard matrices, using the tools of algebraic coding theory and the customary association of linear codes with designs.  ...  The five On the other hand, there is only one equivalence class of 8 x 8 Hadamard matrices, so if we use the Kronecker construction, we must use equivalent matrices.  ... 
doi:10.2307/2154164 fatcat:ddpjtkhtkndmlm5xt6pxu3kbli

The moment map of a Lie group representation

N. J. Wildberger
1992 Transactions of the American Mathematical Society  
This leads naturally to the notion, defined for any prime p , of p-equivalence for Hadamard matrices for which the standard equivalence of Hadamard matrices is, in general, a refinement: for example, the  ...  We study these, and other classes of designs associated with Hadamard matrices, using the tools of algebraic coding theory and the customary association of linear codes with designs.  ...  The five On the other hand, there is only one equivalence class of 8 x 8 Hadamard matrices, so if we use the Kronecker construction, we must use equivalent matrices.  ... 
doi:10.1090/s0002-9947-1992-1040046-6 fatcat:f5xlybg4rfba3be7tyvl6xcz2e

Switching Operations for Hadamard Matrices

William P. Orrick
2008 SIAM Journal on Discrete Mathematics  
To illustrate their power, we use them to greatly improve the lower bounds on the number of equivalence classes of Hadamard matrices in orders 32 and 36 to 3,578,006 and 4,745,357.  ...  These operations have application to the enumeration and classification of Hadamard matrices.  ...  I thank Hadi Kharaghani for extensive correspondence and for providing many unpublished Hadamard matrices in orders 32 and 36.  ... 
doi:10.1137/050641727 fatcat:r5bnjetgm5aqni2f6eyvqngasy

Page 26 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Cocyclic Hadamard matrices and Hadamard groups are equivalent. (English summary) J. Algebra 192 (1997), no. 2, 749-779. In a sequence of papers N. Ito [J.  ...  Flannery proves that cocyclic Hadamard matrices and Hadamard groups are equivalent, via the known relationship be- tween cocycles and transversals in an extension group of {+1} by G.  ... 

An introduction to cocyclic generalised Hadamard matrices

K.J. Horadam
2000 Discrete Applied Mathematics  
In this introduction we outline the necessary background on cocycles and their properties, give some familiar examples of this unfamiliar concept and demonstrate the equivalence of the above-mentioned  ...  We present recent results on the theory of cocyclic generalised Hadamard matrices and their applications in one area: error-correcting codes. ?  ...  A bibliography of publications on cocyclic matrices and cocyclic codes is given in a subsection of the references.  ... 
doi:10.1016/s0166-218x(99)00233-4 fatcat:jmbljn2dsfd3venxh3nhs7yeoe
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