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Experimental Mathematics Volume 7, 1998 - Issue 2
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Original Articles

Extended GCD and Hermite Normal Form Algorithms via Lattice Basis Reduction

George Havas Centre for Discrete Mathematics and Computing, Department of Computer Science and Electrical Engineering, The University of Queensland, Queensland, 4072, Australia E-mail: [email protected]  http://www.it.uq.edu.auh/-avas/
,
Bohdan S. Majewski Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia E-mail: [email protected]  http://wwwcs.newcastle.edu.au/Staff/bohdan/
&
Keith R. Matthews Centre for Discrete Mathematics and Computing, Department of Mathematics, The University of Queensland, Queensland, 4072, Australia E-mail: [email protected]  http://www.maths.uq.edu.au/-krm/
Pages 125-136 | Published online: 03 Apr 2012

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Haocheng Yu, Luyao Yang, Jinyu Dai, Baoping Jiang, Zhengtian Wu & Shuxian Zhu. (2022) Fixed-point iterative approach for solving linear Diophantine systems with bounds on the variables. Cyber-Physical Systems 0:0, pages 1-14.
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Mostafa Khorramizadeh. (2009) A note on solving linear Diophantine systems by using L 3-reduction algorithm. International Journal of Computer Mathematics 86:5, pages 883-896.
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Sándor Z. Kiss & Péter Kutas. (2021) An identification system based on the explicit isomorphism problem. Applicable Algebra in Engineering, Communication and Computing.
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Gook Hwa Cho, Hyang-Sook Lee, Seongan Lim & Yoonjeong Kim. (2021) Storage efficient algorithm for Hermite Normal Form using LLL. Linear Algebra and its Applications 613, pages 183-200.
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Elena Kirshanova, Huyen Nguyen, Damien Stehlé & Alexandre Wallet. (2020) On the smoothing parameter and last minimum of random orthogonal lattices. Designs, Codes and Cryptography 88:5, pages 931-950.
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Peter Overbury, István Z. Kiss & Luc Berthouze. 2019. Complex Networks and Their Applications VII. Complex Networks and Their Applications VII 718 730 .
Yoonjeong Kim, Hyemin Yun & Seongan Lim. (2018) HNF Implementation Strategy Analysis for Lattice Cryptography (Lightning Talk). HNF Implementation Strategy Analysis for Lattice Cryptography (Lightning Talk).
Chuangyin Dang & Yinyu Ye. (2015) A fixed point iterative approach to integer programming and its distributed computation. Fixed Point Theory and Applications 2015:1.
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Simon Hampe. (2014) a-tint : A polymake extension for algorithmic tropical intersection theory. European Journal of Combinatorics 36, pages 579-607.
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Evelyne Hubert & George Labahn. (2013) Scaling Invariants and Symmetry Reduction of Dynamical Systems. Foundations of Computational Mathematics 13:4, pages 479-516.
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J.-M. Couveignes. (2009) Linearizing torsion classes in the Picard group of algebraic curves over finite fields. Journal of Algebra 321:8, pages 2085-2118.
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Karen Aardal & Friedrich Eisenbrand. 2010. The LLL Algorithm. The LLL Algorithm 293 314 .
Denis Simon. 2010. The LLL Algorithm. The LLL Algorithm 265 282 .
Bernhard Beckermann, George Labahn & Gilles Villard. (2006) Normal forms for general polynomial matrices. Journal of Symbolic Computation 41:6, pages 708-737.
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G. Jäger. (2004) Reduction of Smith Normal Form Transformation Matrices. Computing 74:4, pages 377-388.
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George Havas. (2003) On the complexity of the extended euclidean algorithm (Extended Abstract). Electronic Notes in Theoretical Computer Science 78, pages 1-4.
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Adam N Letchford. (2002) Totally tight Chvátal–Gomory cuts. Operations Research Letters 30:2, pages 71-73.
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Frank Lübeck. (2002) On the Computation of Elementary Divisors of Integer Matrices. Journal of Symbolic Computation 33:1, pages 57-65.
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Alexander Bockmayr, Volker Weispfenning & Michael Maher. 2001. Handbook of Automated Reasoning. Handbook of Automated Reasoning 751 842 .
Wilberd Van Der Kallen. (2000) Complexity of the Havas, Majewski, Matthews LLL Hermite Normal Form Algorithm. Journal of Symbolic Computation 30:3, pages 329-337.
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George Havas & Clemens Wagner. 1999. Workshop on wide area networks and high performance computing. Workshop on wide area networks and high performance computing 161 170 .
Gene Cooperman, Sandra Feisel, Joachim von zur Gathen & George Havas. 1999. Computing and Combinatorics. Computing and Combinatorics 310 317 .
George Havas & Jean-Pierre Seifert. 1999. Mathematical Foundations of Computer Science 1999. Mathematical Foundations of Computer Science 1999 103 113 .

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