Index system and separability of constant weight Gray codes

1229 compression of files of information retrieval systems. With this application in mind, bounds on the average codelength of an alphabetical code were studied. The major results of this correspondence are as follows. 1) A necessary and sufficient condition for the existence of a 2) An upper bound for Lopt (the average codelength of the binary alphabetical code was given. optimal alphabetical code) was given. This upper bound shows the redundancy of the optimal alphabetical code in comparison with the Huffman code. Though this correspondence presents a theoretical bound on Lopt, the redundancy of the optimal alphabetical code varies with the distribution of probabilities. To verify the efficiency of the code in practice, the author encoded the descriptors (keywords) of the ERIC thesaurus. There are 8696 descriptors (the average length of a descriptor is about 17 characters), and the alphabet size of the source symbols is 39 (26 capital letters, 10 numeric characters, 2 symbols, and a space character). In this preliminary experiment, L, , and Lop, are 4.254 bits and 4.423 bits, respectively. The redundancy of the optimal alphabetical code is about 5 percent in comparison with the Huffman coding, which shows the usefulness of the alphabetical code. Absfract-A number system is developed for the conversion of natural numbers to the codewords of the Gray code G(n, k) of length n and weight k , and vice versa. As an application sharp lower and upper bounds are derived for the value of li-jl, where i and j are indices of codewords gi and gj of G (n , k) such that they differ in precisely 2m bits.