Crosscorrelation of m-Sequences, Exponential Sums and Dickson Polynomials
Tor Helleseth · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2010
Binary maximal-length sequences (or m-sequences) are sequences of period 2m-1 generated by a linear recursion of degree m. Decimating an m-sequence {st} by an integer d relatively prime to 2m-1 leads to another m-sequence {sdt} of the same period. The crosscorrelation of m-sequences has many applications in communication systems and has been an important and well studied problem during more than 40 years. This paper presents an updated survey on the crosscorrelation between binary m-sequences with at most five-valued crosscorrelation and shows some of the many recent connections of this problem to several areas of mathematics such as exponential sums and Dickson polynomials.