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A constructive solution to a problem of ranking tournaments [article]

Shohei Satake
2019 arXiv   pre-print
In this note, we give a construction of many such tournaments by using skew Hadamard difference sets which have been investigated in combinatorial design theory.  ...  Moreover, we give exponentially many non-isomorphic doubly regular tournaments obtained by a known construction of skew Hadamard difference sets.  ...  We also give exponentially many non-isomorphic examples by using a known construction of skew Hadamard difference sets. At first, we give the definition of skew Hadamard difference sets.  ... 
arXiv:1902.10204v1 fatcat:zykdcrtlxjgxval7yokzo4xo7y

Distortion-free Golden-Hadamard Codebook Design for MISO Systems

Md. Abdul Latif Sarker, Md. Fazlul Kader, Moon Ho Lee, Dong Seog Han
2018 IEEE Communications Letters  
In this letter, a novel Golden-Hadamard codebook (GHC) scheme is proposed to improve the performance of the traditional precoded Alamouti coding for multiple-input and single-output systems.  ...  PROPOSED GPA SCHEME In this section, we will design a distortion-free GPA scheme. For this purpose, we first design a Golden Hadamard precoding matrix.  ...  Many existing works have introduced a Golden number for STBCs, but Golden precoding has not yet been introduced for OSTBCs.  ... 
doi:10.1109/lcomm.2018.2864124 fatcat:ilfcvmhf3ferlia5e35epouyem

Page 5574 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Thus, many problems remain open. {For the entire collection see MR 93m:05005.}  ...  A matrix of order n with entries in {1,—1} and distinct rows orthogonal is called an Hadamard matrix.  ... 

Minimally-Entangled State Preparation of Localized Wavefunctions on Quantum Computers [article]

Natalie Klco, Martin J. Savage
2019 arXiv   pre-print
The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum (| 0〉^⊗ n_Q) and in medium (n_Q-1 qubits initialized to an exponential  ...  In the case of a single site of a non-interacting scalar field theory, initializing to a symmetric exponential wavefunction requires n_Q-1 entangling gates, compared with the 2^n_Q-1 + n_Q-3 + δ_n_Q,1  ...  However, due to residual many-body interactions between the qubits, the in-medium measurement requires a different angular shift to instantiate the copied exponential.  ... 
arXiv:1904.10440v2 fatcat:glomexuxnvaibkucaiw4jhjc2a

Gate-level simulation of quantum circuits

George F. Viamontes, Manoj Rajagopalan, Igor L. Markov, John P. Hayes
2003 Proceedings of the 2003 conference on Asia South Pacific design automation - ASPDAC  
The matrices (operators) representing quantum gates, and vectors modeling qubit states grow exponentially with an increase in the number of qubits.  ...  However, by using a new data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, many of these matrices and vectors can be represented in  ...  Beyond the domain of digital logic design, ROBDD variants have been adopted in many contexts.  ... 
doi:10.1145/1119772.1119829 dblp:conf/aspdac/ViamontesRMH03 fatcat:fqh2v4bwpraehnytj7tmxjv6mu

Performance study and improvement on ECC-based binary anti-collusion forensic code for multimedia

W. Sabrina Lin, Shan He, Jeffrey Bloom
2009 Proceedings of the 11th ACM workshop on Multimedia and security - MM&Sec '09  
The post-processing may introduce errors in the detected bits of the forensic code and represents a new challenge to the forensic code design.  ...  The simulation results show that our binary forensic code design can achieve 100% detection rate when the number of colluders is less than 20 and up to 32% of the colluded forensic code is changed during  ...  In our following results section, we use the Kronecker product of an exponential code with a Hadamard matrix.  ... 
doi:10.1145/1597817.1597834 dblp:conf/mmsec/Lin0B09 fatcat:rhrn6iqhd5a3hn772hthafm3re

On the super-stability of exponential Hilbert-valued functional equations

H Rezaei, M Sharifzadeh
2011 Journal of Inequalities and Applications  
We generalize the well-known Baker's super-stability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product.  ...  the Hadamard product.  ...  We will show that such behavior is typical for approximately exponential mappings with values in Hilbert spaces with Hadamard product which is not multiplicative.  ... 
doi:10.1186/1029-242x-2011-114 fatcat:dxj6qbz2zffsxdzczzv6pziute

Page 3514 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
Exponential lower bounds on the corresponding number of such nonisomorphic linear codes, difference sets and symmetric designs are obtained. G. Berman (Waterloo, Ont.)  ...  Edward Spence (Glasgow) Kantor, William M.(1-OR) 84i:05027 Exponential numbers of two-weight codes, difference sets and symmetric designs. Discrete Math. 46 (1983), no. 1, 95-98.  ... 

On generalized Hadamard matrices of minimum rank

Vladimir D. Tonchev
2004 Finite Fields and Their Applications  
Generalized Hadamard matrices of order q nÀ1 (q-a prime power, nX2) over GF ðqÞ are related to symmetric nets in affine 2-ðq n ; q nÀ1 ; ðq nÀ1 À 1Þ=ðq À 1ÞÞ designs invariant under an elementary abelian  ...  It is likely that these designs yield an exponentially growing number of inequivalent generalized Hadamard matrices over the additive group of GF ðqÞ: However, that appears difficult to prove.  ...  For any prime power q; the number of nonisomorphic affine 2-designs with parameters (1) grows exponentially with n [5] [6] [7] .  ... 
doi:10.1016/j.ffa.2003.11.001 fatcat:p4ecqn5zyjdgtlcxxeyyuyttzu

Interference versus success probability in quantum algorithms with imperfections

Daniel Braun, Bertrand Georgeot
2008 Physical Review A. Atomic, Molecular, and Optical Physics  
For Shor's algorithm, the number of Hadamard gates depends on the implementation of the modular exponentiation and the calculation of the function f , but grows exponentially with the number of qubits  ...  to θ = π/4, while the cases θ = 0 and θ = π/2 replace the Hadamard gates by the Pauli matrices σ z and σ x , respectively, which create no Shor's algorithm there are in general many "good" final states  ... 
doi:10.1103/physreva.77.022318 fatcat:whtord4isbezreao7mg36chc5q

Calculating the thermal rate constant with exponential speedup on a quantum computer

Daniel A. Lidar, Haobin Wang
1999 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The resulting exact algorithm scales exponentially faster with the dimensionality of the system than all known "classical" algorithms for this problem.  ...  Miller for a critical reading of the manuscript and many useful comments, and Dr. Christof Zalka for helpful correspondence. DAL gratefully acknowledges partial support from NSF Grant CHE 97-32758.  ...  energy eigenstates is polynomial) since there are exponentially many position eigenstates |j !  ... 
doi:10.1103/physreve.59.2429 fatcat:5js5p46smzh7lfevrvlkr6sq6y

Structural properties of Hadamard designs [chapter]

Alexander Hulpke, Robert Liebler, Tim Penttila, Ákos Seress
2006 Finite Geometries, Groups, and Computation  
Given the existence of a Hadamard design of order n, we derive an exponential lower bound for the number of non-isomorphic Hadamard designs of order 2n. 2.  ...  This dissertation focusses on structural properties of Hadamard designs. These are designs obtained from Hadamard matrices, which have been crucial objects of combinatorial study for over 100 years.  ...  Exponentially Many Hadamard Designs Let D 1 be a Hadamard design of order n and A 2 be an affine Hadamard design of order n.  ... 
doi:10.1515/9783110199741.141 fatcat:cnqxyjipnbcphhicf72yv3k3fm

Page 4546 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
Working with Whittaker cardinal functions, an exponentially convergent 65 NUMERICAL ANALYSIS 4546 quadrature for Hadamard finite part integrals is obtained.  ...  In many Fou- rier processors a repeated transformation of electronic, optical and acoustic signals into one another takes place.  ... 

Walsh‐Hadamard‐transform‐based SC‐FDMA system using WARP hardware

Shri Ramtej Kondamuri, Anuradha Sundru
2021 ETRI Journal  
This study proposes a new transceiver design for an SC-FDMA system based on Walsh-Hadamard transform (WHT).  ...  The exponential companding technique is used to reduce its PAPR without degrading its BER.  ...  In [7] , a new transceiver design for the SC-FDMA system based on discrete Wavelet transform (DWT) has been proposed.  ... 
doi:10.4218/etrij.2019-0502 fatcat:re2tnjrwsna4llxt26elcdzc54

On probabilistic data association for achieving near-exponential diversity over fading channels

Atulya Yellepeddi, Kyeong Jin Kim, Chunjie Duan, Philip Orlik
2013 2013 IEEE International Conference on Communications (ICC)  
We discuss the use of the probabilistic data association (PDA) detector in conjunction with precoding to design high-performance systems for these links.  ...  We discuss the use of the probabilistic data association (PDA) detector in conjunction with precoding to design high-performance systems for these links.  ...  Proposed Ordering Scheme To design a mechanism for ordering, we consider the space of precoded symbols z = P x.  ... 
doi:10.1109/icc.2013.6655449 dblp:conf/icc/YellepeddiKDO13 fatcat:sw63kwze45hupe3fkrhof6idze
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