Binary Solutions to Some Systems of Linear Equations

  • Alexandr V. SeliverstovEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 871)


A point is called binary if its coordinates are equal to either zero or one. It is well known that it is hard to find a binary solution to the system of linear equations whose coefficients are integers with small absolute values. The aim of the article is to propose an effective probabilistic reduction from the system to the unique equation when there is a small difference between the number of binary solutions to the first equation and the number of binary solutions to the system. There exist nontrivial examples of linear equations with small positive coefficients having a small number of binary solutions in high dimensions.


Subset sum Linear equation Probabilistic algorithm Computational complexity 



The author would like to thank the anonymous reviewers for useful comments.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)MoscowRussia

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