The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$

Families of m-sequences with low correlation property have important applications in communication systems. In this paper, for a prime p ≡ 1 mod 4 and an odd integer k, we study the cross correlation between a p-ary m-sequence {st} of period pn - 1 and its decimated sequence {sdt}, where d = (pk+1)2/2(pe+1), e|k and n = 2k. Using quadratic form polynomial theory, we obtain the distribution of the cross correlation which is six-valued. Specially, our results show that the magnitude of the cross correlation is upper bounded by 2√pn + 1 for p = 5 and e = 1, which is meaningful in CDMA communication systems. © 2013 AIMS.