On the Generating Function and its Application to Ternary Line Codes

One of the major problems researchers face is how to verify experimental or simulation results of any class of codes. Usually this can be done by deriving bounds to test the performance of codes. As they are used in binary codes and especially in linear convolutional codes, where the sum of any two codewords is another codeword and the all-zeros sequence is a codeword, the major step to derive these bounds is to calculate the generating function. Since ternary line codes are non-linear line codes, we will investigate in this paper the possibility of deriving the generating function for at least some of these codes.