SOME RESULTS IN THE THEORY OF ARITHMETIC CODES,
Abstract
The paper presents a simple number-theoretic investigation of the structure of binary arithmetic AN codes. The range (0, B-1) of represented integers is related to the code length n through ((2 to the nth power)-1 = AB). The analysis is based on the partition of the integers 1 = or < N = or < B-1 into orbits, which are analogous to cosets of the multiplicative subgroup of the powers of 2 modulo B. It is shown how the code minimum weight is related to the members of the orbit. The properties of sets of prime powers are used in developing a simple search strategy for codes. An important consequence of the presented analysis is the construction of codes of moderate distance and high rate, thereby filling the spectrum between the two known extremes of the single-error correcting Brown codes and of the maximum-sequence-like codes of Barrows and Mandelbaum. A list of codes of length = or < 36 is finally presented.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1969
- Accession Number
- AD0688835
Entities
People
- Franco P. Preparata
- Robert Tienwen Chien
- S. J. Hong
Organizations
- University of Illinois Urbana–Champaign