In the current paper, we propose a new generalized 'useful' R-norm information measure with two parameters a and b. Some basic properties and the particular cases of this measure are discussed. Further, we define the 'useful' R-norm average code-word length and obtain the bounds in terms of the proposed measure. Huffman coding and Shannon-Fano coding schemes are considered to verify the noiseless coding theorem by taking hypothetical data. Also, we analyze the behaviour of the proposed 'useful' R-norm information and its average code-word length at various values of a , B and R .