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Yongbo XIA Shaoping CHEN Tor HELLESETH Chunlei LI
Let m ≥ 3 be an odd positive integer, n=2m and p be an odd prime. For the decimation factor $d=rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$, the cross-correlation between the p-ary m-sequence {tr1n(αt)} and its all decimated sequences {tr1n(αdt+l)} is investigated, where 0 ≤ l < gcd(d,pn-1) and α is a primitive element of Fpn. It is shown that the cross-correlation function takes values in {-1,-1±ipm|i=1,2,…p}. The result presented in this paper settles a conjecture proposed by Kim et al. in the 2012 IEEE International Symposium on Information Theory Proceedings paper (pp.1014-1018), and also improves their result.
Chunlei LI Nian LI Matthew G. PARKER
Bipolar complementary sequence pairs of Types II and III are defined, enumerated for n ≤ 28, and classified. Type-II pairs are shown to exist only at lengths 2m, and necessary conditions for Type-III pairs lead to a non-existence conjecture regarding their length.