Radioelectronics and Communications Systems

, Volume 62, Issue 3, pp 97–108 | Cite as

Constructive Synthesis Methods of Binary Error Correcting Code of Length 32 for MC-CDMA Technology

  • M. I. Mazurkov
  • A. V. SokolovEmail author


The article proposes the constructive synthesis methods of binary error correcting code of length N = 32 with the optimal value of peak-to-average power ratio of Walsh–Hadamard spectrum for MC-CDMA technology. The authors have developed three constructive methods for the synthesis of codewords of correcting code: in the time domain, in the Walsh–Hadamard transform domain, and in the Reed–Muller transform domain. The parameters of the built code correspond to the best-known codes in McWilliams table.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. G. Paterson, “Sequences for OFDM and Multi-Code CDMA: Two Problems in Algebraic Coding Theory,” in: Helleseth T., Kumar P.V., Yang K. (eds.), Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science (Springer, London, 1982). DOI: Scholar
  2. 2.
    M. Noshad, M. Brandt-Pearce, “Hadamard-coded modulation for visible light communications,” IEEE Trans. Commun. 64, No. 3, 1167 (2016). DOI: Scholar
  3. 3.
    N. Tokareva, Bent Functions: Results and Applications to Cryptography (Academic Press, 2015). URI: Scholar
  4. 4.
    M. I. Mazurkov, A. V. Sokolov, I. V. Tsevukh, “Synthesis method for families of constant amplitude correcting codes based on an arbitrary bent-square,” J. Telecommun. Electronic Computer Eng. 9, No. 2, 99 (2017). URI: Scholar
  5. 5.
    M. I. Mazurkov, A. V. Sokolov, N. A. Barabanov, “Synthesis method for bent sequences in the Vilenkin-Chrestenson basis,” Radioelectron. Commun. Syst. 59, No. 11, 510 (2016). DOI: Scholar
  6. 6.
    M.I. Mazurkov, A. V. Sokolov, “The regular rules of constructing the complete class of bent-sequences of length 16,” Odes’kyi Politechnichnyi Universystet. Pratsi, No. 2, 227 (2013). URI:
  7. 7.
    M. I. Mazurkov, A. V. Sokolov, “Fast orthogonal transformations based on bent-sequences,” Informatics Math. Methods Simulation 4, No. 1, 5 (2014). URI: Scholar
  8. 8.
    M. I. Mazurkov, Wideband Radio Systems [in Russian] (Nauka i Tekhnika, Odessa, 2010).Google Scholar
  9. 9.
    S. V. Agievich, “On the representation of bent functions by bent rectangles,” Proc. of Fifth Int. Petrozavodsk Conf. on Probabilistic Methods in Discrete Mathematics, 1–6 June 2000, Petrozavodsk (VSP, Utrecht, Boston, 2002), pp. 121–135. URI: Scholar
  10. 10.
    S. V. Agievich, “Bent rectangles,” Proc. of NATO Advanced Study Institute on Boolean Functions in Cryptology and Information Security, 8–18 Sept. 2007, Zvenigorod, Russia (IOS Press, Amsterdam, 2008), pp. 3–22. URI: Scholar
  11. 11.
    A. G. Rostovtsev, Cryptography and Protection of Information [in Russian] (Mir i Sem’ya, St. Petersburg, 2002).Google Scholar
  12. 12.
    F. J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes (North Holland Publishing Co., 1977).zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Odessa National Polytechnic UniversityOdessaUkraine

Personalised recommendations