On the decoding of a class of shortened cyclic codes for a compound channel

In a previous paper Hsu (1971), it was pointed out that the shortened cyclic codes generated by g(x) = (xc + 1) g1(x) have the best rate of transmission when it is used as error correcting codes in a compound channel. The shortened cyclic codes are of length N + c where N and c are relatively prime and g1(x) generates a cyclic code of length N with dmin ⩾ 2t + 1. This paper studies the random error decoding algorithms for the shortened cyclic codes. Two random error decoding algorithms are presented.It is also found that if g1(x) generates a maximum length code, then N and c are not required to be relatively prime. The shortened cyclic codes generated can be easily decoded without using the two random error decoding algorithms presented. This result is also reported