Summary: We introduce the concept of ``parallel error correcting'' codes, the error correcting codes for parallel channels. Here, a parallel channel is a set of channels such that the additive error over a finite field occurs in one of its members at time \(T\) if the same error occurs in all members at the same time. The set of codewords of a parallel error correcting code has to be a product set, if the messages transmitted are from independent information sources. We present a simple construction of optimal parallel error correcting codes based on ordinary optimal error correcting codes and a construction of optimal linear parallel codes for independent sources based on optimal ordinary linear error correcting codes. The decoding algorithms for these codes are provided as well.