p-Ary and q-ary versions of certain results about bent functions and resilient functions

Authors:
Xiang-Dong Hou
Affiliations:
Department of Mathematics and Statistics, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435-001, USA
Venue:
Finite Fields and Their Applications
Year:
2004

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Abstract

Using the Teichmuller character and Gauss sums, we obtain the following results concerning p-ary bent functions and q-ary resilient functions: (1) a characterization of certain q-ary resilient functions in terms of their coefficients; (2) stronger upper bounds for the degree of p-ary bent functions; (3) determination of all bent functions on F"p; (4) a characterization of ternary weakly regular bent functions in terms of their coefficients.