Institute of Electrical & Electronic Engineers
The authors devise an analytically simple as well as invertible approximate expression, which describes the relation between the maximum free distance of a binary code and the corresponding maximum attainable code-rate. One of the fundamental open problems in coding theory is constituted by the issue of determining the highest cardinality. In addition to its theoretical significance, the problem considered appears in numerous important applications, including the design of efficient coding schemes and their characterization in terms of the achievable probability of error. Although the complete solution of the rate-versus-free-distance problem does not exist at the time of writing, several theoretical lower and upper bounds on the desired relation may be found in the literature.