New Families of $p$-ary Sequences of Period $\frac{p^n-1}{2}$ With Low Maximum Correlation Magnitude

Let $p$ be an odd prime such that $p\equiv 3\mathrm{m}\mathrm{o}\mathrm{d}4$ and $n$ be an odd integer. In this paper, two new families of $p$-ary sequences of period $N = \frac{p^n-1}{2}$areconstructedbytwodecimated$p$-arym-sequences$m(2t)$and$m(dt)$,where$d = 4$and$d = (p^n + 1)/2=N+1$. The upper bound on the magnitude of correlation values of two sequences in the family is derived using Weil bound. Their upper bound is derived as $\frac{3}{\sqrt{2}} \sqrt{N+\frac{1}{2}}+\frac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.