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FTX Raises $420M in Series B-1 Raise

Extension of a finite field

In a book I am reading mentions the following Suppose that if $q=p^{n}$ for some $p$ and that $F_{q}$ is an extension of $F_{p}$. Because $F_q$ is a vector space of dimension $n$ over $F_p$ , elements of $F_q$ must look like $a = (a_0,…, a_{n − 1})$ where $forall a_i in F_p$ for each::Listen

In a book I am reading mentions the following

Suppose that if $q=p^{n}$ for some $p$ and that $F_{q}$ is an
extension of $F_{p}$. Because $F_q$ is a vector space of dimension $n$
over $F_p$ , elements of $F_q$ must look like $a = (a_0,…, a_{n − 1})$ where
$forall a_i in F_p$ for each $0 leq i leq n − 1$.

I can understand that $F_{q}$ is a vector that consists of $n$ elements from $F_{p}$. What I don’t understand is, what is the role of $q$ here? Because All elements of $F_p$ are $< p$. So, no vector in $F_{q}$ will have any element $ p leq x < q$. Why would I call it $F_q$ if the $q$ doesn’t play any role here?

FTX Raises $420M in Series B-1 Raise

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