Results on generalized negabent functions

Rashmeet Kaur and Deepmala Sharma
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 4, Pages 38–44
DOI: 10.7546/nntdm.2018.24.4.38-44
Full paper (PDF, 166 Kb)

Details

Authors and affiliations

Rashmeet Kaur
Department of Mathematics, National Institute of Technology, Raipur
Raipur, 49010, Chhattisgarh, India

Deepmala Sharma
Department of Mathematics, National Institute of Technology, Raipur
Raipur, 49010, Chhattisgarh, India

Abstract

In this article, we characterize generalized negabent functions on ℤ₂ⁿ with values in ℤ₈ and ℤ₁₆. Furthermore, we propose several constructions of generalized negabent functions.

Keywords

• Boolean function
• Generalized negabent
• Nega-Hadamard transform

2010 Mathematics Subject Classification

• 94A60
• 94C10
• 06E30

References

1. Chaturvedi, A., & Gangopadhyay, A. K. (2013) On Generalized NegaHadamard Transform, In: Singh K., Awasthi A.K. (eds) Quality, Reliability, Security and Robustness in Heterogeneous Networks. QShine 2013. Lectures Notes of the Institute for Computer Sciences, Social Informatics and Telecommunication Engineering, Vol. 115, Springer, Berlin, 771–777.
2. Parker, M. G., & Pott, A. (2007) On Boolean Functions Which Are Bent and Negabent, Sequences, Subsequences and consequences, Lecture Notes in Computer Science, Vol. 4893, Springer, Berlin, 9–23.
3. Rothaus, O. S. (1976) On Bent functions, Journal of Combinatorial Theory, Series A, 20 (3), 300–305.
4. Schmidt, K. U. (2009) Quaternary Constant-Amplitude Codes for Multicode CDMA, IEEE Transactions on Information Theory, 55 (4), 1824–1832.
5. Sole, P., & Tokareva, N. (2009) Connections between Quaternary and Binary Bent Functions, In: Cryptology ePrint Archives, http://eprint.iacr.org/2009/544.pdf.
6. Stanica, P., Martin, T., Gangopadhyay S., & Singh, B. K. (2013) Bent and generalized bent Boolean functions, Designs Codes and Cryptography, 69 (1), 77–94.