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Section Week 9
This is an outline of the topics we covered in the first week of class.
Subsection Tuesday 3/10
It was an exam. No notes today.
Subsection Thursday 3/12
Coding Theorist of the Day.
Sascha Kurz, PhD 2005
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Subspace coding, math. analysis of voting systems, discrete optimization
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Reminders.
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Video Project Report due next Th 11:59 pm
Q: For RS, why \(n \leq q\text{?}\)
\(n = \#\) of distinct evaluation points of poly’s defined over
\(GF(q)\text{,}\) so
\(n \leq |GF(q)| = q\)
Q: Why do we care about RS?
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They are optimal codes! RS codes are MDS
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They decode nicely (post spring break)
Q: Original view vs modern view RS?
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Original view: codewords are
\((p(\alpha_{1}), \dots, p(\alpha_{n}))\)
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Modern view: codewords as polynomials w/ particular roots
Q: Why is it bad that \(n \leq q\text{?}\)
We want a binary code (to send data).
\begin{equation*}
[7, 3, 5]_{2^3}\text{ RS code}\mapsto [21, 9, \geq 5]_{2} \text{ code}
\end{equation*}
