Correctable Errors of Weight Half the Minimum Distance Plus One for the First-Order Reed-Muller Codes

  • Kenji Yasunaga
  • Toru Fujiwara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


The number of correctable/uncorrectable errors of weight half the minimum distance plus one for the first-order Reed-Muller codes is determined. From a cryptographic viewpoint, this result immediately leads to the exact number of Boolean functions of m variables with nonlinearity 2m − 2 + 1. The notion of larger half and trial set, which is introduced by Helleseth, Kløve, and Levenshtein to describe the monotone structure of correctable/uncorrectable errors, plays a significant role in the result.


Syndrome decoding Reed-Muller code correctable error Boolean function nonlinearity larger half 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kenji Yasunaga
    • 1
  • Toru Fujiwara
    • 1
  1. 1.Graduate School of Information Science and Technology, Osaka University, Suita 565-0871Japan

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