Mathematics and Statistics Vol. 10(3), pp. 542 - 548
DOI: 10.13189/ms.2022.100309
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On Generalized Bent and Negabent Functions

Deepmala Sharma *, Sampada Tiwari
National Institute of Technology, Raipur, 492010, Chhattisgarh, India


From the last few years, generalized bent functions gain a lot of attention in research as they have many applications in various fields such as combinatorial design, sequence design theory, cryptography, CDMA communication, etc. A deep and broad study of generalized bent functions with their properties is done in literature. Kumar et al.[11] first gave the concept of generalized bent function. Many researchers studied the properties and characterizations of generalized bent functions. In [2] authors introduced the concept of generalized (-ary) negabent functions and studied some properties of generalized (-ary) negabent functions. In this paper, we study the generalized (-ary) bent functions , where is the ring of integers with mod , is the vector space of dimension over and ≥2 is any positive integer. We discuss several properties of generalized (-ary) bent functions with respect to their nega-Hadamard transform. We also study the relation between generalized nega-Hadamard transforms and generalized nega-autocorrelations. Furthermore, we prove the necessary and sufficient conditions for the bentness and negabentness of generalized (-ary) bent function generated by the secondary construction for , where .

Generalized Bent Function, Generalized Walsh-Hadamard Transform, Generalized Nega-Hadamard Transform

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Deepmala Sharma , Sampada Tiwari , "On Generalized Bent and Negabent Functions," Mathematics and Statistics, Vol. 10, No. 3, pp. 542 - 548, 2022. DOI: 10.13189/ms.2022.100309.

(b). APA Format:
Deepmala Sharma , Sampada Tiwari (2022). On Generalized Bent and Negabent Functions. Mathematics and Statistics, 10(3), 542 - 548. DOI: 10.13189/ms.2022.100309.