Construction and Count of Boolean Functions of an Odd Number of Variables with Maximum Algebraic Immunity
<|reference_start|>Construction and Count of Boolean Functions of an Odd Number of Variables with Maximum Algebraic Immunity: Algebraic immunity has been proposed as an important property of Boolean functions. To resist algebraic attack, a Boolean function should possess high algebraic immunity. It is well known now that the algebraic immunity of an $n$-variable Boolean function is upper bounded by $\left\lceil {\frac{n}{2}} \right\rceil $. In this paper, for an odd integer $n$, we present a construction method which can efficiently generate a Boolean function of $n$ variables with maximum algebraic immunity, and we also show that any such function can be generated by this method. Moreover, the number of such Boolean functions is greater than $2^{2^{n-1}}$.<|reference_end|>
@article{li2006construction,
    title={Construction and Count of Boolean Functions of an Odd Number of
  Variables with Maximum Algebraic Immunity},
    author={Na Li and Wen-Feng Qi},
    journal={arXiv preprint arXiv:cs/0605139},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0605139},
    primaryClass={cs.CR}
}