Computing generating sets of lattice ideals and Markov bases of lattices (original) (raw)
Related papers
Computing generating sets of lattice ideals
A fast algorithm for building lattices
Information Processing Letters, 1999
Computing a Lattice Basis Revisited
Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019
Efficient algorithms on distributive lattices
Discrete Applied Mathematics, 2001
A fast incremental algorithm for building lattices
Journal of Experimental & Theoretical Artificial Intelligence, 2002
Lattice computations for random numbers
Mathematics of Computation, 1999
Order, 1987
An algorithm for dualization in products of lattices and its applications
Algebraic and Euclidean Lattices: Optimal Lattice Reduction and Beyond
ArXiv, 2019
Computing Gröbner bases associated with lattices
Advances in Mathematics of Communications, 2016
Algebraic lattices via polynomial rings
Computational and Applied Mathematics, 2019
Construction piA\pi_ApiA and piD\pi_DpiD Lattices: Construction, Goodness, and Decoding Algorithms
arXiv (Cornell University), 2015
Article electronically published on February 24, 1999 LATTICE COMPUTATIONS FOR RANDOM NUMBERS
2011
Constructions of algebraic lattices
Computational & Applied Mathematics, 2010
Lattices Over Algebraic Integers With an Application to Compute-and-Forward
IEEE Transactions on Information Theory, 2018
Truncated Markov bases and Gr\"obner bases for Integer Programming
2006
Binomial generation of the radical of a lattice ideal
2008
A formula for ideal lattices of general commutative rings
2006
The dependence Graph of a Lattice
Lattice decompositions through methods using congruence relations
2015
The intersection graph of ideals of a lattice
2015
Low-dimensional lattice basis reduction revisited
ACM Transactions on Algorithms, 2009
Integer Programming, Lattices, and Results in Fixed Dimension
Handbooks in Operations Research and Management Science, 2005
Min-Sum algorithm for lattices constructed by Construction D
ArXiv, 2012
Computing the degree of a lattice ideal of dimension one
Journal of Symbolic Computation, 2014
A Theoretical Aspect of Lattice Based Cryptography
A Generic Scheme for the Design of Efficient On-Line Algorithms for Lattices
Mohamed Rouane-hacene, Petko Valtchev
Lecture Notes in Computer Science, 2003
LLL for ideal lattices: re-evaluation of the security of Gentry–Halevi’s FHE scheme
Designs, Codes and Cryptography, 2014
Implementing Candidate Graded Encoding Schemes from Ideal Lattices
Lecture Notes in Computer Science, 2015
Univariate Ideal Membership Parameterized by Rank, Degree, and Number of Generators
arXiv (Cornell University), 2018
A fast and general algorithm for Galois lattices building
2005
Construction πA and πD Lattices: Construction, Goodness, and Decoding Algorithms
IEEE Transactions on Information Theory, 2017
IEEE Signal Processing Magazine, 2011
Lecture Notes : "Topics in Algebraic Computation"
From algebraic sets to monomial linear bases by means of combinatorial algorithms
Discrete Mathematics, 1995