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As a message I get (5,0,1,3), which is coding a sequence of numbers of length 2 in $\mathbb{F}_7$ as polynom with the 4 support points a1 = 0, a2 = 1, a3 = 2, a4 = 6. In the transimission occured an error. Calculate the original message.

How do I do this? In my script we didnt't talked about polynomial codes directly just about the cyclic code. And the topic of this exercise is polynomial codes.

Could someone please get me through this or explain a way? Thanks for any help!

Edit1:

Seems like I need a generator polynom? Right? How do I get it? In my researching it seems like it's a fixed chosen one everywhere?

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