Abstract
Let p, q (p < q) be two odd primes with gcd(p-1, q-1) = 6. In this paper, based on the Whiteman generalized cyclotomy, new generalized cyclotomic sequences with order six and length pq are constructed. We first calculate the autocorrelation values of these sequences and get conditions of p and q such that they are four-valued. Besides, we find some specific examples such that the autocorrelation function takes on only a few values.
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Gong, X., Zhang, B., Feng, D., & Yan, T. (2014). Autocorrelation values of new generalized cyclotomic sequences of order six over Zpq. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8567, pp. 86–98). Springer Verlag. https://doi.org/10.1007/978-3-319-12087-4_6
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