Question: Find a 13-bit burst error polynomial that cannot be detected by the CRC-8 check. The burst error polynomial must have the form E(x) = x^12

Find a 13-bit burst error polynomial that cannot be detected by the CRC-8 check. The burst error polynomial must have the form E(x) = x^12 + + 1, and the terms x^k for k = 1, 2, , 11 can have a coefficient of either 0 or 1. Here is a 13-bit burst error polynomial that can be detected: x^12 + x^8 + x^2 + x + 1. The CRC-8 generator polynomial is x^8 + x^2 + x + 1. (By a 13-bit burst error we mean that there has been a burst of energy that causes noise on the communication channel during the span of 13 bits. For example, the energy may drive the voltage to a high value for all 13 bits. Some of those bits might have been 1s (and represented by the high voltage), so the energy does not cause those bits to be in error. So, assume the first and thirteenth bits are incorrect, and the bits in between those two end points may or may not be in error.)

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