Special issue editorial: Sequences and their applications

Abstract

We are very pleased to introduce this special issue on Sequences and their Applications. Sequences (and arrays, their higher-dimensional relatives) exhibit a strong interplay between theory and application. In one direction, the study of sequences has benefitted greatly from motivating applications in communications, cryptography, coding, and combinatorics. In the other direction, the development of the theory of sequences using tools from finite fields, finite geometry, analysis and number theory has enabled the solution of practical design problems in emerging applications. The purpose of this special issue is to highlight advances in both the theory and application of sequences. The invited paper “A complementary construction using mutually unbiased bases” by G. Wu and M. Parker introduces a previously unrecognized connection between the construction of pairs of (Golay) complementary sequences and arrays, that are particularly valuable in wireless communications, and the mutually unbiased bases of quantum information theory. This novel point of view opens up new directions for research into complementary sequences. The paper “A simple suboptimal construction of cross-bifix-free codes” by D. Bajic and T. Loncar-Turukalo concerns the construction of sets of codewords (sequences) that are suitable for communications synchronization, in the sense that no codeword ends the way another one starts. The paper has both expository and historical value: an earlier version influenced the development of international mobile communications standards as a research report in 2007, but until now its contents have not been made publically available. Cryptogr. Commun. (2014) 6:1–2 DOI 10.1007/s12095-014-0098-1