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We devise an analytically simple as well as invertible approximateexpression, which describes the relation between the minimum distance of abinary code and the corresponding maximum attainable code-rate. For example,for a rate-(1/4), length-256 binary code the best known bounds limit theattainable minimum distance to 65<d(n=256,k=64)<90, while our solution yieldsd(n=256,k=64)=74.4. The proposed formula attains the approximation accuracywithin the rounding error for ~97% of (n,k) scenarios, where the exact value ofthe minimum distance is known. The results provided may be utilized for theanalysis and design of efficient communication systems.

An Approximate Coding-Rate Versus Minimum Distance Formula for Binary Codes