Understanding CRC

There are some documents on the internet describing CRC32 and related algorithms. A Painless Guide to CRC Error Detection Algorithms by Ross Williams explains CRC as an engineer would do explicitly describing what is happening with bits. It also covers reasons of great variety of CRC types. A mathematician would probably be more happy reading an article The iSCSI CRC32C Digest and the Simultaneous Multiply and Divide Algorithm by Luben Tuikov and Vicente Cavanna. CRC is presented rigorously as a division over F_2 field. The second article can lead to an idea how to split CRC calculation over different threads. Same thoughts appear in article Fast Parallel CRC Algorithm and Implementation on a Configurable Processor by H. Michael Ji and Earl Killian.