In a wireless transmission it is necessary to use the channel encoder in order to avoid losses due to transmission errors. This paper presents a method to design the tailbiting codes (TB) for packet data transmission over the additive white gaussian noise (AWGN) channel. In this paper, genetic algorithms (GA) [1] are used in search of good tailbiting codes. The GA technique is applied in search of good binary tailbiting systematic, rate 1/2 and 2/3 convolutional codes concatenated with 4-PSK and 8-PSK modulation and in search of good non binary rate 1/2 convolutional codes over ring Z 4 concatenated with 16-QAM modulation. The search is based on the maximum free Euclidean distance criterion. It is found that the new approach is very effective especially in case of encoders with large number of inputs or with large number of states. Finally, the search results are presented in the tables.