Proof properties of Walsh TransformationIn our lecture notes we're given some properties of Walsh-Transform, for a given mapping f:F2n→F2 (from n-dimensional-Vectorspace over F2 to F2)The Walsh-Transform itself is given as fw(a)=∑x∈F((−1)f(x)+&lt;ax&gt;} with being the inner product of the two vectors a,x. (means ∑inai⋅xi)

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Fastage6bk

2022-02-15

Proof properties of Walsh Transformation
In our lecture notes we're given some properties of Walsh-Transform, for a given mapping

f : F_{2}^{n} \to F_{2}

(from n-dimensional-Vectorspace over F2 to F2)
The Walsh-Transform itself is given as

f^{w} (a) = \sum_{x \in F} ({(- 1)}^{\begin{array}{cc} f (x) + < a & x > \end{array}}}

with being the inner product of the two vectors a,x. (means

\sum_{i}^{n} a_{i} \cdot x_{i}

)

Keenan Mora

Beginner2022-02-16Added 11 answers

This is an instance of Parsevals

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