CRC Codes Based on a Non-Primitive Generator Polynomial: A New Error Control Scheme Targeting a Prescribed Set of Error Patterns

A new approach to error correction codes based on non-primitive cyclic redundancy check (CRC) generator polynomials is introduced. A CRC code can be designed to detect a prescribed set of error patterns that can occur anywhere within the codeword. In this work, we observe that by using a non-primitive generator polynomial, the error pattern can be identified completely (among the prescribed set) and side information on the position of the error event can also be generated. We show that there exists a non-primitive generator polynomial that produces syndromes that can completely specify each prescribed error pattern. Moreover, we show that the computed syndrome can also determine the position of the error event within some sub-block of the codeword.