An updated review on cross-correlation of m-sequences

TL;DR

This paper reviews the extensive research on the cross-correlation properties of m-sequences, highlighting known results, mathematical structures, and open problems for future exploration.

Contribution

It provides a comprehensive summary of all known results on m-sequence cross-correlation spectra and identifies open problems for further research.

Findings

Summarizes all known results on m-sequence cross-correlation spectra.

Highlights the mathematical structures and properties of m-sequences.

Promotes open problems for future research in the field.

Abstract

Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties that are favorable in practical applications. During the past five decades, the crosscorrelation between m-sequences of the same period has been intensively studied, and a particular research focus has been on investigating the cross-correlation spectra with few possibles values. In this chapter we summarize all known results on this topic in the literature and promote several open problems for future research.