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Designs, Codes and Cryptography

, Volume 49, Issue 1–3, pp 323–340 | Cite as

An improved list decoding algorithm for the second order Reed–Muller codes and its applications

  • Rafaël Fourquet
  • Cédric Tavernier
Article

Abstract

We propose an algorithm which is an improved version of the Kabatiansky–Tavernier list decoding algorithm for the second order Reed–Muller code RM(2, m), of length n = 2 m , and we analyse its theoretical and practical complexity. This improvement allows a better theoretical complexity. Moreover, we conjecture another complexity which corresponds to the results of our simulations. This algorithm has the strong property of being deterministic and this fact drives us to consider some applications, like determining some lower bounds concerning the covering radius of the RM(2, m) code.

Keywords

List decoding Reed–Muller codes Covering radius Boolean functions Cryptography 

AMS Classifications

94B05 94B35 94B65 94A60 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Paris 8 Saint-Denis (MAATICAH)Saint-Denis cedexFrance
  2. 2.THALES CommunicationsColombesFrance

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