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Consider functions on the discrete cube $\{-1,1\}^n$. We consider the Discrete Fourier Transform of such functions. Suppose we denote the parity function on a subset $S \subseteq [n]$ of co-...

Let $Q^n := \{0,1\}^n$ be the Hamming cube with the Hamming metric. (Recall that the Hamming is defined by the distance $d(x,y) := \# \{ i : x_i \neq y_i \}$. For integers $0 \leq k \leq n$, define a ...

Tao and Ziegler have introduced a generalization of polynomials over a prime field called nonclassical polynomials, useful for studying the Gowers norm. A nonclassical polynomial of degree $d$ is a ...

For any $c \in \mathbb{F}_2^n$ define $\sigma_c: \mathbb{F}_2^n \to \mathbb{F}_2$ the quadratic polynomial defined for $v = (v_1,v_2,...,v_n)$ by: $$ \sigma_c (v) = \sum_{i=1}^n v_iv_{i+1} + c_iv_i $...