Note: On the degree of homogeneous bent functions

Authors:
Qingshu Meng;Huanguo Zhang;Min Yang;Jingsong Cui
Affiliations:
Computer School, Wuhan University, Hubei 430072, China;Computer School, Wuhan University, Hubei 430072, China;International School of Software, Wuhan University, Hubei 430072, China;Computer School, Wuhan University, Hubei 430072, China
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

In this paper, the degree of homogeneous bent functions is discussed. We prove that for any nonnegative integer k, there exists a positive integer N such that for n=N there exist no 2n- variable homogeneous bent functions having degree n-k or more, where N is the least integer satisfying 2^N^-^1N+10+N+11+...+N+1k+1.