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Sum of binary quadratic forms over inputs of equal Hamming weight
$\DeclareMathOperator{\field}{\mathbb{F}}$
Let $n$ be a positive integer, and let $q : \field_2^{n} \rightarrow \field_2$ be a quadratic form, specified in coordinates as
$$q(x)=\sum_{i =1}^n \alpha_i ...
- 980
2
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Inseparable field extensions of degree p and linear independence
Let $F$ be a field of characteristic $p$; let $\alpha \in F$ such that $\alpha \neq \beta^p$ for any $\beta \in F$, and let $K := F(x)$ where $x=\sqrt[p]{\alpha}$.
Is it true that the elements $1,(x-...
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