Feb 28

Go over homework. Questions about any of that stuff?

OK, so it turns out there are many versions of linear codes :

There is *lots* of crazy math theory in these things.

Discuss a few of the ideas, for example by looking at wikipedia: computation of CRC and wikipedia: polynomial code.

Talk about polynomial division, mod 2.

And see if we can illustrate the connection between (x**n - 1), generating polynomials, and cyclic codes.

 Example: 
   000 110 011 101 
   generated by (1 + x) = (1,1,0)
   identity element (x + x**2) = (0, 1, 1)
   all evenly divide x**3 - 1

Assignment 1 should you decide to accept it: pick one of the above, and investigate.

Remember the point of all these methods: find a tricky set of (linear) codewords that are each a given (hamming) distance apart.

In fact, the online brute-force code generator may be of interest in that context.

Assignment 2 : read the attached 7.8 and shannons theorem.pdf, and come to class Thu ready to explain what it's all about.

http://cs.marlboro.edu/ courses/ spring2012/information/ notes/ Feb_28
last modified Tuesday February 28 2012 11:26 am EST

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