My question is about the CRC generator polynomial.
If I have a generator of level 5, say:
$$X^5+X^4+X^2+1$$
How can I know if it can or cannot detect a parity error?
Also how can I know the error patterns that can pass without being detected?
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\$\begingroup\$ What exactly do you mean by "parity error"? In its most general sense, it means any odd number (1, 3, 5, ...) of bits have been flipped. \$\endgroup\$ – Dave Tweed♦ Apr 10 '14 at 17:59
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This is a general rule , in youre case k = 6
Short Burst Errors
(Length b ≤ k, number of redundant bits)
-->All errors up to length k are detected
- Long Burst Errors (Length b = k+1)
Undetectable only if burst error is the same as g(x)
g(x) = x^k+ … + 1 k-1 bits between xk and x0
e(x) = x^k + … + 1 must match
Probability of not detecting the error is 2^(-(k-1))
- Longer Burst Errors (Length m > k+1)
Probability of not detecting the error is 2^(-k)
