On the ranks of bent functions

Authors:
Guobiao Weng;Rongquan Feng;Weisheng Qiu
Affiliations:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China;LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China;LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China
Venue:
Finite Fields and Their Applications
Year:
2007

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Abstract

The rank of a bent function is the 2-rank of the associated symmetric 2-design. In this paper, it is shown that it is an invariant under the equivalence relation among bent functions. Some upper and lower bounds of ranks of general bent functions, Maiorana-McFarland bent functions and Desarguesian partial spread bent functions are given. As a consequence, it is proved that almost every Desarguesian partial spread bent function is not equivalent to any Maiorana-McFarland bent function.