%0 Journal Article
%T An Approximate Coding-Rate Versus Minimum Distance Formula for Binary Codes
%A Yosef Akhtman
%A Robert G. Maunder
%A Lajos Hanzo
%J Mathematics
%D 2012
%I arXiv
%X We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4), length-256 binary code the best known bounds limit the attainable minimum distance to 65<d(n=256,k=64)<90, while our solution yields d(n=256,k=64)=74.4. The proposed formula attains the approximation accuracy within the rounding error for ~97% of (n,k) scenarios, where the exact value of the minimum distance is known. The results provided may be utilized for the analysis and design of efficient communication systems.
%U http://arxiv.org/abs/1206.6584v1