Loading...
Search for:
group-actions
0.005 seconds
Spectral classification and multiplicative partitioning of constant-weight sequences based on circulant matrix representation of optical orthogonal codes [electronic resource]
, Article IEEE Transactions on Information Theory ; 2010 vol. 56, no. 9 ; Salehi, Jawad A ; $item.subfieldsMap.a ; Sharif University Of TechnologySpectral classification and multiplicative partitioning of constant-weight sequences based on circulant matrix representation of optical orthogonal codes
, Article IEEE Transactions on Information Theory ; Volume 56, Issue 9 , 2010 , Pages 4659-4667 ; 00189448 (ISSN) ; Salehi, J. A ; Sharif University of Technology
Abstract
Considering the space of constant-weight sequences as the reference set for every optical orthogonal code (OOC) design algorithm, we propose a classification method that preserves the correlation properties of sequences. First, we introduce the circulant matrix representation of optical orthogonal codes and, based on the spectrum of circulant matrices, we define the spectral classification of the set Sn,w of all (0, 1)-sequences with length n, weight w, and the first chip 1. Then, as a method for spectrally classifying the set Sn,w, we discuss an algebraic structure called multiplicative group action. Using the above multiplicative group action, we define an equivalence relation on Sn,w in...
Standardness of Einstein Solvmanifolds
, M.Sc. Thesis Sharif University of Technology ; Fanai, Hamid Reza (Supervisor)
Abstract
In this thesis, we review the proof to standardness of Einstein solvamanifolds which is based on some results from Geometric Invariant Theory and stratification of topological spaces. Standardness is a very simple and yet powerful algebraic condition on the lie algebra of a solvmanifold which yields to remarkable existence and uniqueness and obstruction results