# American Institute of Mathematical Sciences

May  2018, 12(2): 303-315. doi: 10.3934/amc.2018019

## Several infinite families of p-ary weakly regular bent functions

 1 School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, China 2 School of Mathematics and Information, China West Normal University, Sichuan Nanchong, 637002, China 3 School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China

* Corresponding author: Chunming Tang

Received  November 2016 Published  March 2018

Fund Project: This work is supported by the National Natural Science Foundation of China (Grant No. 11401480, 11701129, 11571285, 11531002). C. Tang also acknowledges support from 14E013, CXTD2014-4 and the Meritocracy Research Funds of China West Normal University. Z. Zhou and C. Fan are in part supported by the National Cryptography Development Fund under Grant MMJJ20170119. Y. Qi also acknowledges support from Zhejiang provincial Natural Science Foundation of China (LQ17A010008, LQ16A010005).

As an optimal combinatorial object, bent functions have been an interesting research object due to their important applications in cryptography, coding theory, and sequence design. The characterization and construction of bent functions are challenging problems in general. The objective of this paper is to present a construction of p-ary weakly regular bent functions from known weakly regular bent functions. This generalizes some earlier constructions of Boolean bent functions and p-ary bent functions, and produces several infinite families of p-ary weakly regular bent functions from known ones. Some infinite families of p-ary rotation symmetric bent functions are obtained as well.

Citation: Yanfeng Qi, Chunming Tang, Zhengchun Zhou, Cuiling Fan. Several infinite families of p-ary weakly regular bent functions. Advances in Mathematics of Communications, 2018, 12 (2) : 303-315. doi: 10.3934/amc.2018019
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