Further crosscorrelation properties of sequences with the decimation factor d=fracpn+1p+1-fracpn-12{d=frac{p^n+1}{p+1}-frac{p^n-1}{2}}

摘要

For an odd integer n ≥ 3, an odd prime p ≡ 3(mod4) and d=fracpn+1p+1-fracpn-12{d=frac{p^n+1}{p+1}-frac{p^n-1}{2}}, the value distribution of the exponential sum å_{x Î mathbbFpn *}wTrn₁(x-gxd) (g Î mathbbF_pn*){sumlimits_{xin mathbb{F}_{p^n}^{,*}}omega^{Tr^n_1(x-gamma x^{d})},(gammain mathbb{F}_{p^n}^{*})} is completely determined in this paper, where ω is a primitive complex p-th root of unity. This improves the results of Müller (1999) and Hu et al. (2001) about the crosscorrelation of sequences with the decimation factor d.