On cross-correlation spectrum of generalized bent functions in generalized Maiorana-McFarland class

2013 ◽  
Vol 2 (3) ◽  
pp. 139-145 ◽  
Author(s):  
Brajesh Kumar Singh
Keyword(s):  
Cross Correlation ◽  
Bent Functions ◽  
Generalized Bent Functions ◽  
Correlation Spectrum

New Constructions of Codebooks Nearly Meeting the Welch Bound

2020 ◽  
Vol 31 (07) ◽  
pp. 875-889
Author(s):  
Zexia Shi ◽  
Lei Sun ◽  
Fang-Wei Fu
Keyword(s):  
Positive Integer ◽  
Code Division Multiple Access ◽  
Multiple Access ◽  
Bent Functions ◽  
Welch Bound ◽  
Generalized Bent Functions ◽  
Multiple Access Communications ◽  
Generic Construction ◽  
Direct Spread ◽  
Code Division Multiple

Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented.

scholarly journals The Super Luminous Maser Source in the Nucleus of NGC 3079

1988 ◽  
Vol 129 ◽  
pp. 233-234
Author(s):  
Aubrey D. Haschick ◽  
Willem A. Baan ◽  
Matthew H. Schneps ◽  
Mark J. Reid ◽  
James M. Moran
Keyword(s):  
Water Vapor ◽  
Cross Correlation ◽  
Phase Variation ◽  
Owens Valley ◽  
Correlation Spectrum ◽  
The Galaxy ◽  
The Cross

On 1984 October 6 we conducted a 3-station intercontinental Mark II VLBI experiment in order to study the very luminous water vapor maser source in the nucleus of the galaxy NGC 3079, which was detected first by Haschick and Baan (1985) using the Haystack Observatory 36.6 m antenna. The cross correlation spectrum for the longest Owens Valley to MPI baseline is presented in Figure 1 and shows the phase variation across the width of the brightest feature at 955.7 km s−1 to be less than 10 degrees of phase.

scholarly journals Following Forrelation – quantum algorithms in exploring Boolean functions' spectra

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Suman Dutta ◽  
Subhamoy Maitra ◽  
Chandra Sekhar Mukherjee
Keyword(s):  
Boolean Functions ◽  
Cross Correlation ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Sampling Technique ◽  
Linear Functions ◽  
Query Complexity ◽  
Walsh Spectrum ◽  
Correlation Spectrum ◽  
The Cross

<p style='text-indent:20px;'>Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al., 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation spectrum, and the autocorrelation spectrum. We introduce the existing 2-fold Forrelation formulation with bent duality-based promise problems as desirable instantiations. Next, we concentrate on the 3-fold version through two approaches. First, we judiciously set up some of the functions in 3-fold Forrelation so that given oracle access, one can sample from the Walsh Spectrum of <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula>. Using this, we obtain improved results than what one can achieve by exploiting the Deutsch-Jozsa algorithm. In turn, it has implications in resiliency checking. Furthermore, we use a similar idea to obtain a technique in estimating the cross-correlation (and thus autocorrelation) value at any point, improving upon the existing algorithms. Finally, we tweak the quantum algorithm with the superposition of linear functions to obtain a cross-correlation sampling technique. This is the first cross-correlation sampling algorithm with constant query complexity to the best of our knowledge. This also provides a strategy to check if two functions are uncorrelated of degree <inline-formula><tex-math id="M2">\begin{document}$ m $\end{document}</tex-math></inline-formula>. We further modify this using Dicke states so that the time complexity reduces, particularly for constant values of <inline-formula><tex-math id="M3">\begin{document}$ m $\end{document}</tex-math></inline-formula>.</p>

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