Solution

Cyclic Redundancy Check (CRC). It is one of the widely used parity bit based error detection scheme. It is a special number is appended to a block of data in order to detect any changes introduced during storage (or transmission). The CRC is recalculated on retrieval / reception and compared to the value originally transmitted, which can reveal certain types of error.

CRC presentation is based on -

• Polynomial Division
• Arithmetic over the field of integers mod 2 - Here, the arithmetic over the field of integers mod 2 is arithmetic on single bit binary numbers with all overflows ignored.

For all the errors to be found in an odd number of inverted bits, the condition should be that (x + 1) is a factor of G(x).