In this research, recurrent codes used to correct bursts of error have been studied in detail. A mathematical formulation of these codes is presented which shows them to be convolutional codes. The encoding and decoding procedures are presented mathematically, and practical methods of implementation are given. The work of Wyner, Hagelbarger, and Berlekamp is reviewed and discussed. A new class of codes with low transmission rate is presented, and the merits of these codes are discussed. A procedure for construction of a generalized code from known codes is presented, and two theorems concerning this construction are proved. Finally, the advantages of various codes with different rates are examined carefully.