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

Abstract

Let $p$ be an odd prime such that $p\equiv 3\mathrm{mod}4$ and $n$ be an odd integer. In this paper, two new families of $p$-ary sequences of period $N=\frac{p^n-1}{2}$ are constructed by two decimated $p$-ary m-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.

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