Finite fields
Another Proof of Kasami‘s Theorem
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
On Cosets of Weight 4 of Binary BCH Codes with Minimum Distance 8 and Exponential Sums
Problems of Information Transmission
Crosscorrelation properties of binary sequences with ideal two-level autocorrelation
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Niho type cross-correlation functions via dickson polynomials and Kloosterman sums
IEEE Transactions on Information Theory
Further results on m-sequences with five-valued cross correlation
IEEE Transactions on Information Theory
On the correlation distribution of Delsarte---Goethals sequences
Designs, Codes and Cryptography
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Finding the cross correlation between two m-sequences {st} and {sdt} of the same period 2m - 1, that differ by a decimation d, has been a popular research problem since the 1960s. Many cases with three- and four-valued correlation have been determined. Several values of d are known to lead to five-valued cross correlation but their exact correlation distribution has been open. The correlation distribution is completely determined for one of these families with five-valued cross correlation by using evaluations of certain exponential sums including Kloosterman sums. The decimation considered is the special decimation d = 22k+1/2k+1 where m is odd and k = 1, i.e., d = 5/3. The paper introduces some techniques that may be useful to obtain further results on related decimations.