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Two definitions of the Reed-Muller code

I found two definitions Reed-Muller codes being used in literature. More specifically for any $n \in \mathbb{Z}^+$ and $1 \leq d \leq n$ we define the set $RM(d,n)$ in two possible ways, 1. $RM(d,n) =...
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Number of words within Hamming distance $\delta$

This is a problem I'm having reading Arora & Barak's book, page 378-379. They define: For two words $x, y \in \{0, 1\}^m$, the fractional Hamming distance of $x$ and $y$ is equal to the ...
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Application of Expander Codes

I need to give a talk about expander codes at university (I'm a student of computer science). Since they have been introduced to show a family of codes looking good when thinking of the Shannon ...