Lattice Basis Reduction

2011 ◽  
Author(s):  
Murray R. Bremner
Keyword(s):  
Lattice Basis Reduction ◽  
Basis Reduction

Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction

2017 ◽  
Vol 86 (5) ◽  
pp. 1023-1038 ◽  
Author(s):  
Weihua Liu ◽  
Andrew Klapper ◽  
Zhixiong Chen
Keyword(s):  
Synthesis Problem ◽  
Lattice Basis Reduction ◽  
Basis Reduction

scholarly journals Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction

2012 ◽  
Vol 81 (279) ◽  
pp. 1487-1511 ◽  
Author(s):  
Xiao-Wen Chang ◽  
Damien Stehlé ◽  
Gilles Villard
Keyword(s):  
Perturbation Analysis ◽  
Lattice Basis Reduction ◽  
Basis Reduction

scholarly journals Mordell’s equation: a classical approach

2015 ◽  
Vol 18 (1) ◽  
pp. 633-646 ◽  
Author(s):  
Michael A. Bennett ◽  
Amir Ghadermarzi
Keyword(s):  
Lower Bounds ◽  
Diophantine Equation ◽  
Classical Approach ◽  
Linear Forms In Logarithms ◽  
Lattice Basis Reduction ◽  
Linear Forms ◽  
Basis Reduction

We solve the Diophantine equation$Y^{2}=X^{3}+k$for all nonzero integers$k$with$|k|\leqslant 10^{7}$. Our approach uses a classical connection between these equations and cubic Thue equations. The latter can be treated algorithmically via lower bounds for linear forms in logarithms in conjunction with lattice-basis reduction.

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