Let G(x) be the generator polynomial used for CRC checking. What is the condition that should be satisfied by G(x) to detect odd number of bits in error?

For a generator polynomial G(x) used in CRC (Cyclic Redundancy Check) to detect an odd number of bit errors, the polynomial must satisfy the condition that it includes the factor (x + 1). Specifically, G(x) has the ability to detect all odd numbers of bit errors if and only if (G(x)) is divisible by (x + 1). This is because (x + 1) represents a polynomial that, in binary, corresponds to the pattern 11 (i.e., an error of two bits). Multiplying this by any polynomial of even weight (even number of 1s) will result in a polynomial of even weight that captures odd numbers of errors. This property ensures that any error pattern with an odd number of flipped bits will result in a non-zero remainder when divided by (G(x)), thereby indicating the presence of errors.