For quadratic rotation-symmetric Boolean functions, balancedness is determined by the 2-adic valuation of the number of variables, and the monomial functions have explicit weight-recursion polynomials.
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
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abstract
In the literature, few constructions of $n$-variable rotation symmetric bent functions have been presented, which either have restriction on $n$ or have algebraic degree no more than $4$. In this paper, for any even integer $n=2m\ge2$, a first systemic construction of $n$-variable rotation symmetric bent functions, with any possible algebraic degrees ranging from $2$ to $m$, is proposed.
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Affine equivalence for quadratic rotation symmetric Boolean functions
For quadratic rotation-symmetric Boolean functions, balancedness is determined by the 2-adic valuation of the number of variables, and the monomial functions have explicit weight-recursion polynomials.