Deep Singh
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India.

Anjali Chawla
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India.

Pramod Bhogta
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, India.

Amit Paul
Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India.

DOI https://doi.org/10.33889/IJMEMS.2024.9.2.019

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Abstract

In design of secure cryptosystems and CDMA communications, the negabent functions play a significant role. The generalized Boolean functions have been extensively studied by Schmidt and established several important results in this setup. In this paper, several characteristics of the generalized nega-Hadamard transform (GNT) of generalized Boolean functions like inverse of GNT, generalized nega-cross correlation, generalized nega-Parseval’s identity, relationship between GNT and generalized nega-cross correlation have analyzed. We studied the GNT for the derivative of this setup of functions and established the connection of generalized Walsh-Hadamard transform and GNT of derivatives of these functions. Also, the GNT of composition of vectorial Boolean function and generalized Boolean function is presented. Further, the generalized nega-convolution theorem for generalized Boolean function is obtained.

Keywords- Generalized nega-Hadamard transform (GNT), Generalized negabent function, Generalized nega-cross correlation, Generalized boolean function.

Citation

Singh, D., Chawla, A., Bhogta, P., & Paul, A. (2024). A Characterization of Generalized Boolean Functions Employed in CDMA Communications. International Journal of Mathematical, Engineering and Management Sciences, 9(2), 352-365. https://doi.org/10.33889/IJMEMS.2024.9.2.019.