Mixed radix Reed-Muller expansions

Ashur Rafiev, Andrey Mokov, Frank Burns, Julian Murphy, Albert Kolemans, Alex Yakovlev

Research output: Contribution to journalArticle

8 Citations (Scopus)


The choice of radix is crucial for multi-valued logic synthesis. Practical examples, however, reveal that it is not always possible to find the optimal radix when taking into consideration actual physical parameters of multi-valued operations. In other words, each radix has its advantages and disadvantages. Our proposal is to synthesise logic in different radices, so it may benefit from their combination. The theory presented in this paper is based on Reed-Muller expansions over Galois field arithmetic. The work aims to firstly estimate the potential of the new approach and to secondly analyse its impact on circuit parameters down to the level of physical gates. The presented theory has been applied to real-life examples focusing on cryptographic circuits where Galois Fields find frequent application. The benchmark results show the approach creates a new dimension for the trade-off between circuit parameters and provides information on how the implemented functions are related to different radices.
Original languageEnglish
Article number5953584
Pages (from-to)1-15
Number of pages15
JournalIEEE Transactions on Computers
Issue number8
Publication statusPublished - 2012

ASJC Scopus subject areas

  • Hardware and Architecture
  • Software
  • Computational Theory and Mathematics
  • Theoretical Computer Science

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    Cite this

    Rafiev, A., Mokov, A., Burns, F., Murphy, J., Kolemans, A., & Yakovlev, A. (2012). Mixed radix Reed-Muller expansions. IEEE Transactions on Computers, 61(8), 1-15. [5953584]. https://doi.org/10.1109/TC.2011.124