Bent functions

a class of Boolean functions with the maximal possible nonlinearity

have applications in the fields of different sets

combinatorial theory

sequence design and cryptography.Motivated by the design of optimally correlated sequences used in code division multiple access（CDMA） communication system

Kumar et al.Generalized the notion of Boolean bent functions to the case of functions over an arbitrary finite field in 1985.The present paper firstly studied the ranks of circulant matrices over finite field with odd characteristic

based on which we gave a sufficient and necessary condition for bentness of a class of p-ary functions derived from quadratic forms

among which some new p-ary Bent functions were generated.