32-Bit Cyclic Redundancy Code Polynomial

A 32-bit cyclic redundancy code is a type of algebraic polynomial in x with coefficients from a set A of binary numbers. It is used to detect accidental alterations of data during coding and decoding. Castagnoli's results on the algorithmic selection of CRC provide codes which can detect up to 5 errors. In this study we use polynomial algebra over the field and the geometry of the code space to model a class of 32-bit CRC polynomials which can detect up to 7 errors.