New Families of pp-ary Sequences of Period pn−12\frac{p^n-1}{2} With Low Maximum Correlation Magnitude

Let $p$ be an odd prime such that $p \equiv 3\;{\rm mod}\;4$ 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.Comment: 9 page, no figure

New polyphase sequence families with low correlation derived from the Weil bound of exponential sums,”Preprint

In this paper, the sequence families of which maximum correlation is determined by the Weil bound of exponential sums are revisited. Using the same approach, two new constructions with large family sizes and low maximum correlation are given. The first construction is an analogue of one recent result derived from the interleaved structure of Sidel’nikov sequences. For a prime p and an integer M|(p − 1), the new M-ary sequence families of period p are obtained from irreducible quadratic polynomials and known power residue-based sequence families. The new sequence families increase family sizes of the known power residue-based sequence families, but keep the maximum correlation unchanged. In the second construction, the sequences derived from the Weil representation are generalized, where each new sequence is the element-wise product of a modulated Sidel’nikov sequence and a modulated trace sequence. For positive integers d < p and M|(p n − 1), the new family consists of (M − 1)p nd sequences with period p n − 1, alphabet size Mp, and the maximum correlation bounded by (d + 1) √ p n + 3. Index Terms. Character, correlation, exponential sum, m-sequences, power residue sequences