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

Published online by Cambridge University Press:  20 November 2018

Betty Tang ,
Solomon W. Golomb  and
Ronald L. Graham
Betty Tang
Affiliation:
University of Southern California, Los Angeles, California
Solomon W. Golomb
Affiliation:
University of Southern California, Los Angeles, California
Ronald L. Graham
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey
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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, (a1a2 … ak), where

for fixed positive integers k and n, is said to be a comma-free dictionary if and only if, whenever (a1a2 … ak) and (b1b2 … bk) 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 3 , 01 June 1987 , pp. 513 - 526
Copyright
Copyright © Canadian Mathematical Society 1987

References

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