In my book there's an example of how to do a cyclic redundancy check with regular numbers. I've tried to complete the exercise with binary numbers but without success. In the book the given polynomial equals $x^{14}+x^{12}+x^8+x^7+x^5$ and the used generator polynomial is $x^5+x^4+x^2+1$. The result of the question was $x^3+x^2+x$.
The professor included in his powerpoint that 010100011010000 is the starting message en that the remainder in binary should be 01110. The rest was up to us.
I've practiced with different binary messages and I could complete those but I got stuck on this one.
Here's what i've tried so far. When I try to convert the given polynomial into a message it has one zero more. Also my remainder is 00001 and not 01110. I wrote a program to do the calculations for me to see if i made any errors and looked online for a tool that could do it for me but both give me the same result:00001. Whatever I do I can't seem to get the right result. Thanks in advance guys.
Well, the polynomial division of $x^{14}+x^{12}+x^8+x^7+x^5$ by $x^5+x^4+x^2+1$ yields the remainder $x^3+x^2+x$ where the polynomials are defined over $GF(2)$. I've checked this using SINGULAR:
x3+x2+x