Cross-Correlation between a p-Ary m-Sequence and Its All Decimated Sequences for $d=\frac{(p^{m}+1)(p^{m}+p-1)}{p+1}$

抄録

Let m ≥ 3 be an odd positive integer, n=2m and p be an odd prime. For the decimation factor $d=\frac{(p^{m}+1)(p^{m}+p-1)}{p+1}$, the cross-correlation between the p-ary m-sequence {tr₁ⁿ(α^t)} and its all decimated sequences {tr₁ⁿ(α^dt+l)} is investigated, where 0 ≤ l < gcd(d,pⁿ-1) and α is a primitive element of F_pⁿ. It is shown that the cross-correlation function takes values in {-1,-1±ip^m|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.