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The crosscorrelation of maximal length linear shift register sequences is a well-studied problem that has many applications in sequence designs. This problem is known to have many important connections to exponential sums. In recent years, the study of p-ary bent functions has received a lot of attention and several new functions have been found that are related to the crosscorrelation function and that lead to new connections and problems on Jacobsthal sums. This paper gives a survey of some of these connections.

Crosscorrelation of m-sequences, exponential sums, bent functions and Jacobsthal sums