The values of two classes of Gaussian periods in index 2 case and weight distributions of linear codes
The values of two classes of Gaussian periods in index 2 case and weight distributions of linear codes
<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ l $\end{document}</tex-math></inline-formula> be a prime with <inline-formula><tex-math id="M2">\begin{document}$ l\equiv 3\pmod 4 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ l\ne 3 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ N = l^m $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M5">\begin{document}$ m $\end{document}</tex-math></inline-formula> a positive integer, <inline-formula><tex-math id="M6">\begin{document}$ f = \phi(N)/2 $\end{document}</tex-math></inline-formula> the multiplicative order of a prime <inline-formula><tex-math id="M7">\begin{document}$ …