On cyclotomic generator of order r
Information Processing Letters
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
New M-ary sequence families with low correlation and large size
IEEE Transactions on Information Theory
On the Autocorrelation Distributions of Sidel'nikov Sequences
IEEE Transactions on Information Theory
Cross Correlation of Sidel'nikov Sequences and Their Constant Multiples
IEEE Transactions on Information Theory
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It is well known that the magnitude of the cross correlation between any distinct constant multiple sequences of an M-ary power residue sequence of period p is upper bounded by √p + 2 and that of an M-ary Sidel'nikov sequence of period pm - 1 is upper bounded by √pm + 3, where p is a prime and m is a positive integer. In this paper, we first show that their cross-correlation functions are closely related to Jacobi sums and cyclotomic numbers. We then derive the cross-correlation distribution of constant multiple sequences of an M-ary power residue sequence. In the case of constant multiple sequences of an M-ary Sidel'nikov sequence, we get the possible cross-correlation values whose occurrence numbers are expressed in terms of the cyclotomic numbers of order M and are possibly zero.