The author discusses the use of (n, n-1) polynomial codes for data retransmission and bit error rate (BER) monitoring in nonbinary data transmission systems. For a particular type of polynomial code, called a simple polynomial code, a simple error detection scheme which exploits the Gray coding commonly employed in nonbinary data transmission systems can be devised. Even though its algebraic structure is the same as that of general (n, n-1) polynomial code, the simple polynomial code's performance, when using this detection algorithm, is either equal to or better than that of the corresponding general polynomial code, for data retransmission and BER monitoring. The improvement in the BER monitoring performance of the simple code relative to that of the corresponding general code increases as the data alphabet size becomes larger.>