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2 questions
4
votes
1
answer
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Can we explicitly compute this "shift"-quantity over Boolean functions $u:\mathbb{F}_2^n\rightarrow \mathbb{F}_2$?
This question is a follow-up of this question.
Let $\mathbb{F}_2=\{0,1\}$ be the field with two elements, and suppose that $n$ is odd.
Question: Can we compute the exact minimum $$A:=
\min_{u:\mathbb{...
- 6,741
9
votes
1
answer
425
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Are there functions $\mathbb{F}_2^n \to \mathbb{F}_2$ satisfying these special relations?
Let $\mathbb{F}_2=\{0,1\}$ be the field with two elements, and let
$u:\mathbb{F}_2^n\rightarrow \mathbb{F}_2$. Suppose that $n$ is odd.
Is it possible that
$$
\sum_{x \in \mathbb{F}_2^n}(-1)^{u(x)+u(...
- 6,741