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Cyclic Codes over Z3

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    How many cyclic codes of length 4 are there over Z3? Write down two such codes that are different, but each have 9 codewords.

    2. Relevant equations

    number of codewords of length 4 over Z3 = 3^4 = 81

    Not sure about how to refine this to just being the number of cyclic codes

    Maybe I need to view codewords as polynomials?

    3. The attempt at a solution

    Unsure where to start. I think that an example of one of these cyclic codes could be {0000,1111,2222} and this is also a linear code of length 4 in Z3.

    Every time i try to work out a possible answer for the second part, I end up with way too many codewords.

    please help... :)
     
  2. jcsd
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