The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Sueli I. R. Costa - One of the best experts on this subject based on the ideXlab platform.
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Commutative Group codes in r4 r6 r8 and r16 approaching the bound
Discrete Mathematics, 2013Co-Authors: Carina Alves, Sueli I. R. CostaAbstract:Abstract Spherical codes in even dimensions n = 2 m generated by a Commutative Group of orthogonal matrices can be determined by a quotient of m -dimensional lattices when the sublattice has an orthogonal basis. We discuss here the existence of orthogonal sublattices of the lattices A 2 , D 3 , D 4 and E 8 , which have the best packing density in their dimensions, in order to generate families of Commutative Group codes approaching the bound presented in Siqueira and Costa (2008) [14] .
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Optimum Commutative Group codes
Designs Codes and Cryptography, 2013Co-Authors: Cristiano Torezzan, João E. Strapasson, Sueli I. R. Costa, Rogério Monteiro De SiqueiraAbstract:A method for finding an optimum $$n$$ n -dimensional Commutative Group code of a given order $$M$$ M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric Commutative Group codes. Several examples of optimum Commutative Group codes are also presented.
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Commutative Group codes in R4,R6,R8 and R16—Approaching the bound
Discrete Mathematics, 2013Co-Authors: Carina Alves, Sueli I. R. CostaAbstract:Abstract Spherical codes in even dimensions n = 2 m generated by a Commutative Group of orthogonal matrices can be determined by a quotient of m -dimensional lattices when the sublattice has an orthogonal basis. We discuss here the existence of orthogonal sublattices of the lattices A 2 , D 3 , D 4 and E 8 , which have the best packing density in their dimensions, in order to generate families of Commutative Group codes approaching the bound presented in Siqueira and Costa (2008) [14] .
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Flat tori, lattices and bounds for Commutative Group codes
Designs Codes and Cryptography, 2008Co-Authors: Rogério Monteiro De Siqueira, Sueli I. R. CostaAbstract:We show that Commutative Group spherical codes in R n , as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.
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upper bounds for Commutative Group codes the odd case
IEEE International Telecommunications Symposium, 2006Co-Authors: Monteiro R De Siqueira, Sueli I. R. CostaAbstract:Good spherical codes must have large minimum squared distance. An important quota in the theory of spherical codes is the maximum number of points M(n, ρ) displayed on the sphere Sn-1, having a minimum squared distance ρ. The aim of this work is to study this problem restricted to the class of Group codes. We establish a tighter bound for the number of points of a Commutative Group code in odd dimension, extending the bounds of [6].
En Hui Shi - One of the best experts on this subject based on the ideXlab platform.
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The nonexistence of sensitive Commutative Group actions on dendrites
Acta Mathematica Sinica English Series, 2010Co-Authors: En Hui Shi, Bin Yong Sun, Li Zhen ZhouAbstract:In this paper, using the integral method observed by Mai Jiehua recently, we show that no dendrite admits a sensitive Commutative Group action.
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Graphs admitting transitive Commutative Group actions
Topology and its Applications, 2010Co-Authors: Jie-hua Mai, En Hui ShiAbstract:Abstract Let X be a compact metric space, and Homeo ( X ) be the Group consisting of all homeomorphisms from X to X. A subGroup H of Homeo ( X ) is said to be transitive if there exists a point x ∈ X such that { k ( x ) : k ∈ H } is dense in X. In this paper we show that, if X = G is a connected graph, then the following five conditions are equivalent: (1) Homeo ( G ) has a transitive Commutative subGroup; (2) G admits a transitive Z 2 -action; (3) G admits an edge-transitive Commutative Group action; (4) G admits an edge-transitive Z 2 -action; (5) G is a circle, or a k-fold loop with k ⩾ 2 , or a k-fold polygon with k ⩾ 2 , or a k-fold complete bigraph with k ⩾ 1 . As a corollary of this result, we show that a finite connected simple graph whose automorphism Group contains an edge-transitive Commutative subGroup is either a cycle or a complete bigraph.
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The nonexistence of sensitive Commutative Group actions on graphs
Science in China Series A: Mathematics, 2007Co-Authors: Jie-hua Mai, En Hui ShiAbstract:In this paper, we observe a special kind of continuous functions on graphs. By estimating the integrals of these functions, we prove that there are no sensitive Commutative Group actions on graphs. Furthermore, we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it, which answers negatively a question proposed by Kato in 1993.
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The nonexistence of expansive Commutative Group actions on Peano continua having free dendrites
Topology and its Applications, 2007Co-Authors: Jie-hua Mai, En Hui ShiAbstract:A dendrite D in a metric space X is said to be free if there exists a connected open set U in X such that U = D. In this paper, we prove that there is no expansive Commutative Group action on any Peano continuum having a free dendrite. In particular, no 1-dimensional compact ANR admits an expansive Commutative Group action. © 2007 Elsevier B.V. All rights reserved. MSC: primary 54H20; secondary 37B05
Joost Renes - One of the best experts on this subject based on the ideXlab platform.
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ASIACRYPT (3) - CSIDH: an efficient Post-Quantum Commutative Group Action
Lecture Notes in Computer Science, 2018Co-Authors: Wouter Castryck, Tanja Lange, Chloe Martindale, Lorenz Panny, Joost RenesAbstract:We propose an efficient Commutative Group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes–Rostovtsev–Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field \(\mathbb F_p\), rather than to ordinary elliptic curves. The Diffie–Hellman scheme resulting from the Group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.
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csidh an efficient post quantum Commutative Group action
International Conference on the Theory and Application of Cryptology and Information Security, 2018Co-Authors: Wouter Castryck, Tanja Lange, Chloe Martindale, Lorenz Panny, Joost RenesAbstract:We propose an efficient Commutative Group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes–Rostovtsev–Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field \(\mathbb F_p\), rather than to ordinary elliptic curves. The Diffie–Hellman scheme resulting from the Group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.
B. Mityagin - One of the best experts on this subject based on the ideXlab platform.
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Weakly Wandering Vectors for Unitary Actions of Commutative Groups
Journal of Functional Analysis, 1994Co-Authors: Vitaly Bergelson, Isaac Kornfeld, B. MityaginAbstract:Abstract We extend the main result of [V. Bergelson, I. Kornfeld, and B. Mityagin, Proc. Amer. Math. Soc. 119 (1993), 1127-1134.] to more general Commutative Group actions satisfying different mixing conditions. The more general setup required introduction of new techniques based on spectral theory as well as refinement of those used in that paper.
Peter V. Danchev - One of the best experts on this subject based on the ideXlab platform.
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Commutative weakly nil neat Group rings
Communications in Algebra, 2020Co-Authors: Peter V. Danchev, Mahdi SamieiAbstract:Let R be a ring and let G be a Group. We prove a rather curious necessary and sufficient condition for the Commutative Group ring RG to be weakly nil-neat only in terms of R,G and their sections. T...
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THE NUMBER OF IDEMPOTENTS IN Commutative Group RINGS
Journal of Algebra and Its Applications, 2012Co-Authors: Peter V. DanchevAbstract:Let R be a Commutative unital ring of arbitrary characteristic and let G be a multiplicative Abelian Group. For the Group ring RG we completely calculate the number (finite or infinite) of its idempotents only in terms of R, G and their sections. This strengthens our previous results in Sarajevo J. Math. (2011) and Filomat (2012).
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idempotent units of Commutative Group rings
Communications in Algebra, 2010Co-Authors: Peter V. DanchevAbstract:We find a necessary and sufficient condition for every normalized unit in a Commutative unitary Group ring to be an idempotent unit. Our criterion reduces the general situation to the torsion case. This extends in some way results due to Karpilovsky [7, 8] and Danchev [1-3].
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WARFIELD INVARIANTS IN Commutative Group RINGS
Journal of Algebra and Its Applications, 2009Co-Authors: Peter V. DanchevAbstract:We calculate, only in terms of a Commutative unital ring R of prime characteristic p and an abelian p-mixed Group G, the classical Warfield q-invariants Wα,q(VR(G)) of the Group VR(G) of all normalized units in the Group ring R(G). This continues our results in (Extr. Math., 2005), (Collect. Math., 2008) and (J. Alg. Appl., 2008).
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On idempotent units in Commutative Group rings
2009Co-Authors: Peter V. DanchevAbstract:We flnd a necessary and su-cient condition when each normalized unit in a Commutative modular Group ring of prime characteristic p can be decomposed as a p-torsion unit and an idempotent unit. This somewhat strengthens our recent results from (An. Univ. Bucuresti, Mat., 2005 and 2008) as well as from (Kochi Math. J., 2009).