In this paper, we have derived lower and upper bounds of a parametric mean length of code words weighted with the functions of utilities and power probabilities in terms of a new proposed function of the type Tsallis (1988) entropy used in physics under certain condition. Bhaker and Hooda (1993), Kullback-Leibler's (1951), Shannon's (1948) entropy etc. are shown to be a particular case of this new function.