论文信息 - Characterization of $m$-Sequences of Lengths $2^{2k}-1$ and $2^{k}-1$ With Three-Valued Cross Correlation

Characterization of $m$-Sequences of Lengths $2^{2k}-1$ and $2^{k}-1$ With Three-Valued Cross Correlation

Considered is the distribution of the cross correlation between in-sequences of length 22k -1, where m = 2k, and m-sequences of shorter length 2k -1. New pairs of m -sequences with three-valued cross correlation are found and the complete correlation distribution is determined. Finally, we conjecture that there are no more cases with a three-valued cross correlation apart from the ones proven here.

[1] Tor Helleseth,et al. Some results about the cross-correlation function between two maximal linear sequences , 1976, Discret. Math..

[2] Tor Helleseth,et al. Codes with the same coset weight distributions as the Z4-linear Goethals codes , 2001, IEEE Trans. Inf. Theory.

[3] Hans Dobbertin,et al. New cyclic difference sets with Singer parameters , 2004, Finite Fields Their Appl..

[4] Antonia W. Bluher,et al. On xq+1+ax+b , 2004, Finite Fields Their Appl..

[5] T. Kasami. WEIGHT DISTRIBUTION FORMULA FOR SOME CLASS OF CYCLIC CODES , 1966 .

[6] Tor Helleseth,et al. Niho type cross-correlation functions via dickson polynomials and Kloosterman sums , 2006, IEEE Transactions on Information Theory.

[7] H. Niederreiter,et al. Finite Fields: Encyclopedia of Mathematics and Its Applications. , 1997 .

[8] Tor Helleseth,et al. Cross correlation of m-sequences of different lengths , 2006, IEEE Transactions on Information Theory.

[9] H. Dobbertin. Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets , 1999 .

[10] Tor Helleseth,et al. A New Three-Valued Cross Correlation Between$m$-Sequences of Different Lengths , 2006, IEEE Transactions on Information Theory.

[11] Guang Gong,et al. Constructions of quadratic bent functions in polynomial forms , 2006, IEEE Transactions on Information Theory.

[12] K. Conrad,et al. Finite Fields , 2018, Series and Products in the Development of Mathematics.