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ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS
Authors: Qingshu Meng, Huanguo Zhang, Min Yang, Jingsong CuiAbstract:
It is well known that the degree of a 2m-variable bent function
is at most m. However, the case in homogeneous bent functions is
not clear. In this paper, it is proved that there is no
homogeneous bent functions of degree m in 2m variables when
m>3; there is no homogenous bent function of degree m-1 in 2m
variables when m>4; Generally, for any nonnegative integer k,
there exists a positive integer N such that when m>N, there is
no homogeneous bent functions of degree m-k in 2m variables.
In other words, we get a tighter upper bound on the degree of
homogeneous bent functions. A conjecture is proposed that for any
positive integer k>1, there exists a positive integer N such
that when m>N, there exists homogeneous bent function of degree
k in 2m variables.
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