Status of three classes of sequences

• Published in: Cryptography and communications Vol. 15; no. 2; pp. 257 - 308
• Main Authors: Gong, G., Wang, Z.L.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2023; Springer Nature B.V
• Subjects: Circuits; Coding and Information Theory; Combinatorial analysis; Communications Engineering; Computer Science; Cryptography; Data Structures and Information Theory; Digital computers; Fields (mathematics); Fourier analysis; Harmonic analysis; Information and Communication; Linear feedback shift registers; Mathematics of Computing; Networks; Number theory; Pseudorandom sequences; Sputnik satellites; Surveys (invitation only); Pseudorandom sequences; 2-level autocorrelation; Golay complementary sequence sets and complete complementary codes; 05B10; 05B20; Ambiguity function; 11L05; 11L07; 94A55
• ISSN: 1936-2447; 1936-2455
• DOI: 10.1007/s12095-022-00585-4

Pseudorandom sequences, sometimes shortened as sequences, have played a key role in the applications of digital communications, cryptography and computer science. This research field is an example of scientific research directly born from the real world applications. Specifically, the research on sequences stems from the application of the sequences generated by maximal length linear feedback shift registers to detect returning signals from Explorer 1, the satellite launched on January 31, 1958 by US, shortly after Sputnik, launched by Soviet Union on October 4, 1957 which is the first satellite in the human being civilization. With more than seven decades of the developments of theory and practice of sequences, this field has evolved to acquire a wide range of the tools and methodologies from extremely deep mathematic fields (comparing with other engineering subjects), such as algebraic geometry, number theory, combinatorics, representation theory, harmonic analysis, to just mention a few. In this survey, we present the current status of the research in sequence design along three different directions, i.e., the sequences with 2-level autocorrelation, the sequence sets with low ambiguity, and Golay complementary sequence sets and complete complementary codes.