# CRC polynomial and Parity Error detection

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?

• 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. – Dave Tweed Apr 10 '14 at 17:59

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)