A code for positive integers with grouping of message length using geometric progression

A positive integer code EX'E-b,E-h,E-d(b greater than or equal to 1, h grea ter than or equal to 1,d greater than or equal to 0) is proposed. Its codew ord for a positive integer it consists of three kinds of information: (1) h ow many times the number of n's digits can be subtracted by the terms of a progression including a geometric progression, (2) the rest of the subtract ions, and (3) given value of the positive integer n. EX'E-b,E-h,E-d is a no n-recursive type code. It is an asymptotically optimal code (for d greater than or equal to 1) and preserves the lexicographic, length, and number ord ers (for b greater than or equal to h + 2). Some examples of EX'E-b,E-h,E-d are also presented. Their codeword lengths are found to be shorter than th e Amemiya and Yamamoto code CEk except for small positive integers.