Geodesic
Relationship between the coefficients of polynomials over $\mathrm{GF}(2^n)$ and weights of Boolean functions represented by them
Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 28-46.

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Boolean functions in $n$ variables are represented by polynomials over $\mathrm{GF}(2^n)$. The relationship between the coefficients of polynomials and the weights of functions are researched. Some formulas for expressing the dependence of the first and the second bits in the binary code of the function weight on the polynomial coefficients are obtained. For weights of bent functions and for their subfunctions, some expressions are also obtained.
Keywords: Boolean function, bent function, polynomial over a field, vector space, weight of function, subspaces. 
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A. S. Kuzmin; V. I. Nozdrunov. Relationship between the coefficients of polynomials over $\mathrm{GF}(2^n)$ and weights of Boolean functions represented by them. Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 28-46. http://geodesic.mathdoc.fr/item/PDM_2014_4_a3/

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