Cryptography and Communications

, Volume 10, Issue 2, pp 277–289 | Cite as

Classification and Construction of quaternary self-dual bent functions

  • Lin Sok
  • MinJia ShiEmail author
  • Patrick Solé
Part of the following topical collections:
  1. Special Issue on Sequences and Their Applications


Quaternary self-dual bent functions are studied from the viewpoints of existence, construction, and symmetry. A search algorithm is described to classify their orbits under the orthogonal group in low dimensions. A connection with self-dual bent Boolean functions shows that they do not exist in odd number of variables.


Boolean functions Bent functions Walsh Hadamard transform Gray map Rayleigh quotient 

Mathematics Subject Classification (2010)




The first author is supported by China Postdoctoral Science Foundation funded project (2016M601991), and the second author (corresponding author) is supported by NNSF of China (61672036), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2015D11) and Key projects of support program for outstanding young talents in Colleges and Universities (gxyqZD2016008). We thank the referees for their helpful remarks and comments.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiPeople’s Republic of China
  2. 2.Department of MathematicsRoyal University of Phnom PenhPhnom PenhCambodia
  3. 3.Key Laboratory of Intelligent Computing & Signal Processing, Ministry of EducationAnhui UniversityHefei Anhui ProvincePeople’s Republic of China
  4. 4.National Mobile Communications Research LaboratorySoutheast UniversityNanjingPeople’s Republic of China
  5. 5.CNRS/ LAGAUniversity Paris 8Saint-DenisFrance

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