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A simple suboptimal construction of cross-bifix-free codes

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Abstract

Cross-bifix-free sets are sets of bifix-free sequences with the property that no prefix of any sequence is a suffix of any other sequence. This paper presents a general construction method for cross-bifix-free sequences based on kernels. The cardinality of cross-bifix-free sets follows the Fibonacci progression. A simplified method, applicable to a limited number of so-called “regular kernel sets”, is proposed as well. Properties of such sequences with an outline for further research are discussed.

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Notes

  1. Here and elsewhere below, we shall say that simulation occurs when a segment of the data - which may be considered to be random—happens to reproduce a suffix or prefix of a synchronization sequence.

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Acknowledgments

The authors wish to thank the unknown Referee for his helpful and inspiring comments.

This paper is funded in part by Grants TR32040, Ministry of Science, Serbia and 114-451-2061/2011-01 of APV; it is an outcome of COST 2100 and IC1004 Actions.

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Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, 21000, Novi Sad, Serbia

    Dragana Bajic & Tatjana Loncar-Turukalo

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  1. Dragana Bajic
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  2. Tatjana Loncar-Turukalo
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Correspondence to Dragana Bajic.

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Bajic, D., Loncar-Turukalo, T. A simple suboptimal construction of cross-bifix-free codes. Cryptogr. Commun. 6, 27–37 (2014). https://doi.org/10.1007/s12095-013-0088-8

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