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
A family of m-sequences with five-valued cross correlation
IEEE Transactions on Information Theory
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
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
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Recently, the complete five-valued cross-correlation distribution has been determined between two m-sequences {St} and {Sdt} of periods 2m -1 that differ by the decimation d = 22k+1/2k+1 where m is odd and k =1, i.e., d = 5/3. In this paper, the correlation distribution is given in terms of some exponential sums for any k when gcd (k, m) = 1 and m is odd. Furthermore, two new conjectures on exponential sums are presented that are of interest in their own right. Proving these conjectures would imply that the correlation distribution is independent of k under the conditions above and thus the same as for the case k = 1. The conjectures are proven for m odd and k = 2 and the paper gives a new result that the correlation distribution for d = 17/5 is the same as for d = 5/3.