On the hardness of the Lee syndrome decoding problem-Reference-Cited by-同舟云学术

On the hardness of the Lee syndrome decoding problem

Published:2022 Issue:0 Volume:0 Page:0
ISSN:1930-5346
Container-title:Advances in Mathematics of Communications
language:
Short-container-title:AMC

Author:

Weger Violetta¹,Khathuria Karan²,Horlemann Anna-Lena³,Battaglioni Massimo⁴,Santini Paolo⁴,Persichetti Edoardo⁵

Affiliation:

1. Department of Electrical and Computer Engineering, Technical University of Munich, Theresienstrasse 90, 80333, München, Germany

2. Institute of Computer Science, University of Tartu, 51009 Tartu, Estonia

3. School of Computer Science, University of St. Gallen, Dufourstrasse 50, CH-9000 St. Gallen, Switzerland

4. Department of Information Engineering, Marche Polytechnic University, Via Brecce Bianche 12, 60131 Ancona, Italy

5. Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA

Abstract

<p style='text-indent:20px;'>In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the <inline-formula><tex-math id="M1">\begin{document}$ 3 $\end{document}</tex-math></inline-formula>-dimensional matching problem. Then, we study the complexity of solving the problem, by translating the best known solvers in the Hamming metric over finite fields to the Lee metric over finite rings, as well as proposing some novel solutions. For the analyzed algorithms, we assess the computational complexity in the asymptotic regime and compare it to the corresponding algorithms in the Hamming metric.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory,Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory

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