self doubt

Question

CRC can detect any odd number of errors.

CRC can detect all burst errors of less than the degree of the polynomial.

Please explain and if possible give proof

Answer 1

If talk about error detection method CRC and CS (Check Sum) both are not 100% reliable.

Let's come to the question,

1.  If  (data bit + error handling bit )  both are corrupted then the error is called Meaningful error and in this case, None can detect it.

Let's take there are n bits of data and k bits of CRC the possible number of data will be 2^n and CRC set will be 2^k. In real 2^k <<<< 2^n. There is many to one function between them. 

2. According to the above explanation, CRC can detect all burst errors of less than the degree of the polynomial.