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A New Result on Comma-Free Codes of Even Word-Length

Comma-free codes were first introduced in [1] in 1957 as a possible genetic coding scheme for protein synthesis. The general mathematical setting of such codes was presented in [3], and the biochemical and mathematical aspects of the problem were later summarized and extended in [4]. Using the notation of [3], a set D of k-tuples or k-letter words, (a 1 a 2 … a k ), where for fixed positive integers k and n, is said to be a comma-free dictionary if and only if, whenever (a 1 a 2 … a k ) and (b 1 b 2 … b k ) are in D, the “overlaps” are not in D. This precludes codewords having a subperiod less than k; and two codewords which are cyclic permutations of one another cannot both be in D.