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Regent Results in Comma-Free Codes

Published online by Cambridge University Press:  20 November 2018

B. H. Jiggs
B. H. Jiggs*
Affiliation:
California Institute of Technology
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A set D of k-letter words is called a comma-free dictionary (2), if whenever (a1a2 . . . ak) and (b1b2 . . . bk) are in D, the "overlaps" (a2a3 . . . akb1), (a3a4 . . . akb1b2), . . . , (akb1 . . . bk-1) are not in D. We say that two k-letter words are in the same equivalence class if one is a cyclic permutation of the other. An equivalence class is called complete if it contains k distinct members. Comma-freedom is violated if we choose words from incomplete equivalence classes, or if more than one word is chosen from the same complete class.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 178 - 187
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Golomb, S. W., Proceedings of the Symposium on Mathematical Problems in the Biological Sciences, 1961, Amer. Math. Soc. (to appear).Google Scholar
2. Golomb, S. W., Basil Gordon, and Welch, L. R., Comma-free codes, Can. J. Math., 10 (1958), 202–209.Google Scholar
3. Golomb, S. W., Welch, L. R., and Delbrück, M., Construction and properties of comma-free codes, Biol. Medd. Dan. Vid. Selsk., 23, no. 9 (1958).Google Scholar
4. Jaynes, E. T., Note on unique decipherability, IRE Transactions on Information Theory (Sept. 1959), 98-102.Google Scholar