  An efficient scheme to increase the performance of polar codes at short and
moderate block lengths is a concatenation of CRC code and a polar code. In
order to obtain better result of the concatenation, a CRC code with best error
control performance among all CRC codes with a fixed number of check bits has
to be used. In this work we investigate CRC codes of 11 to 19 parity bits and
determine those of them which have maximum minimum distance at any length it
can be used. For CRC codes of 24 parity bits we were not able to perform
complete search and we present the best obtained results. The investigation
shows that there are better CRC polynomials of degrees 11, 16 and 24 than those
suggested by the 3rd Generation Partnership Project (3GPP).
